Explanation: (1) Use the trigonometric formula, cos (a + b) = cos a cos b – sin a sin b and substitute a = b = x. Now write cos 2 x + sin 2 x for 1 on the right side of the equation, (2) Multiply the equation cos2x = cos 2 x - sin 2 x by negative 1 and add 1 on both sides. 🏼 https://integralsforyou.com - Integral of 1/cos^2(x) - How to integrate it step by step using integration by substitution!🚶 𝐒𝐭𝐞𝐩𝐬00:00 Substitution...幂简约公式. 从解余弦二倍角公式的第二和第三版本得到。. 正弦. 餘弦. 其他. sin 2 θ = 1 − cos 2 θ 2 \sin ^ {2}\theta = {\frac {1-\cos 2\theta } {2}} cos 2 θ = 1 + cos 2 θ 2 \cos ^ {2}\theta = {\frac {1+\cos 2\theta } {2}} sin 2 θ cos 2 θ = 1 − cos 4 θ 8 \sin ^ {2}\theta \cos ^ {2 ...A. Công thức cos2x. B. Hàm số y = cos2x. Tập xác định của hàm số y = cos2x. Tập giá trị của y = cos2x. Tính chẵn lẻ của hàm số y = cos2x. Chu kì tuần hoàn của hàm số y = cos2x. C. Đồ thị hàm số y = cos2x. D. Đạo hàm cos2x. E. Nguyên hàm cos2x.You don't have to memorize all formulas but it helps to do so. If you remember, 1 = cos^2 x + sin^2 x. So we have, cos^2 x = 1 - sin^2 x and sin^2 x = 1 - cos^2 x. If we replace cos^2 x in the first double angle formula cos2x = cos^2 x - sin^2 x with 1 - sin^2 x we get: cos2x = 1 - 2 sin^2 x. Free trigonometric equation calculator - solve trigonometric equations step-by-stepCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... Teks video. 1 Min Cos 2 X per 1 + cos 2x = sebelum kita kerjakan soal berikut perlu kita ingat kembali bahwa cos 2x kita bisa berubah menjadi 1 min 2 Sin kuadrat X sehingga 1 Min Cos 2 e-paper 1 + cos 2x bisa kita rubah menjadi 1 Min cos 2x nya kita bahas 1 min 2 Sin kuadrat X per 1 + cos 2x ditambah 1 Min Sin kuadrat X kemudian 1 dikurang 1 habis kemudian Min ketemu Min jadinya + 2 SinX per 1 ... Precalculus. Solve for x 2cos (x)-1=0. 2cos (x) − 1 = 0 2 cos ( x) - 1 = 0. Add 1 1 to both sides of the equation. 2cos(x) = 1 2 cos ( x) = 1. Divide each term in 2cos(x) = 1 2 cos ( x) = 1 by 2 2 and simplify. Tap for more steps... cos(x) = 1 2 cos ( x) = 1 2. Take the inverse cosine of both sides of the equation to extract x x from inside ...Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... Jul 21, 2023 · Step by step video solution for int(1+ cos^2(x))/(1+cos(2x))dx by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams. Ab Padhai karo bina ads ke Khareedo DN Pro and dekho sari videos bina kisi ad ki rukaavat ke! cos^2 x + sin^2 x = 1. sin x/cos x = tan x. You want to simplify an equation down so you can use one of the trig identities to simplify your answer even more. some other identities (you will learn later) include -. cos x/sin x = cot x. 1 + tan^2 x = sec^2 x. 1 + cot^2 x = csc^2 x. hope this helped! Free trigonometric identity calculator - verify trigonometric identities step-by-step 1. To provide a correction to your own work I would remove the lim at first because I want to simplifies to the maximum the expression and at the last the computation, as follows: 1 − cos x x 2 = 2 sin 2 ( x 2) x 2 = 2 x 2 ⋅ sin 2 ( x 2) ( x 2) 2 ⋅ ( x 2) 2 = sin 2 ( x 2) ( x 2) 2 ⋅ 1 2. therefore. lim 1 − cos x x 2 = lim sin 2 ( x 2 ...sin(2X) = 2 sinX cosX cos(2X) = 1 - 2sin 2 X = 2cos 2 X - 1 tan(2X) = 2tanX / [ 1 - tan 2 X ] Multiple Angle Formulas sin(3X) = 3sinX - 4sin 3 X cos(3X) = 4cos 3 X - 3cosX sin(4X) = 4sinXcosX - 8sin 3 XcosX cos(4X) = 8cos 4 X - 8cos 2 X + 1 x^{2}-x-6=0-x+3\gt 2x+1; line\:(1,\:2),\:(3,\:1) f(x)=x^3; prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x) \frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120) \lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx \sum_{n=0}^{\infty}\frac{3}{2^n} Show More Dec 6, 2021 · $\int \frac {1}{\cos^2 x}\,dx=\int \sec^2 x=\tan x +c$ based directly on the list of immediate integrals. The other day a student asked me if we can evaluate the integral using a method like integration by substitution or integration by parts. The only 'solution' I found uses the differentiation of quotient working backwards. I.e. Let us equate, X and Y, i.e. X = Y. So, the above formula for cos 2X, becomes. cos 2X = cos(X + X) = cos X cos X– sin X sin X. cos 2X = cos2 X–sin2 X. Hence, the first cos 2X formula follows, as. cos 2X = cos2 X–sin2 X. And for this reason, we know this formula as double the angle formula, because we are doubling the angle.🏼 https://integralsforyou.com - Integral of 1/cos^2(x) - How to integrate it step by step using integration by substitution!🚶 𝐒𝐭𝐞𝐩𝐬00:00 Substitution...$\int \frac {1}{\cos^2 x}\,dx=\int \sec^2 x=\tan x +c$ based directly on the list of immediate integrals. The other day a student asked me if we can evaluate the integral using a method like integration by substitution or integration by parts. The only 'solution' I found uses the differentiation of quotient working backwards. I.e.Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... 1 Answer. Chandra S. Aug 14, 2015. cos x = - 1/2 = cos 2 π /3 ⇒ x = 2 π /3.1 Answer (s) Available. Find the integration of the expression as per attachment. 1 Answer (s) Available. Integrate whole root of x- alpha/ beta - alpha lower limit =alpha and upper limit = beta. 1 Answer (s) Available. Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-stepWhat are the formulae of (1) 1 + cos2x (2) 1 cos2x Get the answer to this question and access a vast question bank that is tailored for students.Precalculus. Solve for ? cos (x)^2-1=0. cos2 (x) − 1 = 0 cos 2 ( x) - 1 = 0. Add 1 1 to both sides of the equation. cos2(x) = 1 cos 2 ( x) = 1. Take the specified root of both sides of the equation to eliminate the exponent on the left side. cos(x) = ±√1 cos ( x) = ± 1. Any root of 1 1 is 1 1. cos(x) = ±1 cos ( x) = ± 1.simplify\:\tan^4(x)+2\tan^2(x)+1; simplify\:\tan^2(x)\cos^2(x)+\cot^2(x)\sin^2(x) Show More; Description. Simplify trigonometric expressions to their simplest form ... Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-stepsin^2x + cos^2x = 1 the identity known is sin^2x + cos^2x = 1. this can be rearranged to give 1 - cos^2x = sin^2x. using the 'difference of two squares' identity ...Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...In this video I will prove cos^2(x)=(1+cos2x)/2. Course Index. What Is The Unit Circle? The Unit Circle and The Angle (Part 1 of 2) The Unit Circle and The Angle ...In trigonometry formulas, we will learn all the basic formulas based on trigonometry ratios (sin,cos, tan) and identities as per Class 10, 11 and 12 syllabi. Also, find the downloadable PDF of trigonometric formulas at BYJU'S. Trigonometry. Solve for ? cos (x)=-1/2. cos (x) = − 1 2 cos ( x) = - 1 2. Take the inverse cosine of both sides of the equation to extract x x from inside the cosine. x = arccos(−1 2) x = arccos ( - 1 2) Simplify the right side. Tap for more steps... x = 2π 3 x = 2 π 3. The cosine function is negative in the second and third quadrants. It is indeed true that sin2(x)= 1 −cos2(x) and that sin2(x)= 21−cos(2x). How do you use the half-angle identities to find all solutions on the interval [0,2pi) for the equation sin2x = cos2(2x) ? 3π,π and 3.5π Explanation: Use cos2a = 2cos2a−1 . The given equation is sin2x = 1−cos2x = 1−(2cos2(2x)−1)2 = cos2(2x) ...If n > 1 is a positive integer, then: cos^n x = (cos x)^n This is a convenience of notation, to avoid having to use parentheses to distinguish, for example: (cos x)^2 and cos (x^2) By convention we can write: cos^2 x and cos x^2 respectively, without ambiguity. However, in the case of -1, we have a clash of notation.In this video I will prove cos^2(x)=(1+cos2x)/2. Course Index. What Is The Unit Circle? The Unit Circle and The Angle (Part 1 of 2) The Unit Circle and The Angle ...Develop the left side: #LS = (cos^2 x)/(sin^2 x) - cos ^2 x = ((cos^2 x)(1 - sin^2 x))/(sin^2 x) =# #= (cos^2 x.cos^2 x)/(sin^2 x) = cot^2 x.cos^2 x# Proved.In trigonometry formulas, we will learn all the basic formulas based on trigonometry ratios (sin,cos, tan) and identities as per Class 10, 11 and 12 syllabi. Also, find the downloadable PDF of trigonometric formulas at BYJU'S. Feb 10, 2017 · This simplifies to sinx. Use sin^2theta + cos^2theta = 1 -> sin^2theta = 1- cos^2theta and csctheta = 1/sintheta. =(sin^2x)(cscx) = (sin^2x)(1/sinx) = sinx Hopefully this helps! cos2x + cosx − 1 = 0 we obtain. cosx = 1 2( − 1 ± √5). and. sinx = √ 1 2( − 1 + √5) Putting this results into the big equation. sin12x + ⋯ + sin6x we obtain the answer. Example. (√ 1 2( − 1 + √5))16 = 1 2 (47 −21√5) so the answer is.Nov 15, 2015 · 1 Answer. George C. Nov 15, 2015. Use cos2x +sin2x = 1 to find: 1 − cos2x sinx = sinx. Show algebraically cos2x = cos^2x - sin^2x using the sum and difference identities. Verify the Identity: cos^2 t/sin t = csc t - sin t. Verify the identity: 1 - (cos^2 x)/ (1 - sin x) = -sin x. Verify that the equation is an identity. cos 2x + 1 = 2 cos^2 x. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.Precalculus. Solve for ? cos (x)^2-1=0. cos2 (x) − 1 = 0 cos 2 ( x) - 1 = 0. Add 1 1 to both sides of the equation. cos2(x) = 1 cos 2 ( x) = 1. Take the specified root of both sides of the equation to eliminate the exponent on the left side. cos(x) = ±√1 cos ( x) = ± 1. Any root of 1 1 is 1 1. cos(x) = ±1 cos ( x) = ± 1.You don't have to memorize all formulas but it helps to do so. If you remember, 1 = cos^2 x + sin^2 x. So we have, cos^2 x = 1 - sin^2 x and sin^2 x = 1 - cos^2 x. If we replace cos^2 x in the first double angle formula cos2x = cos^2 x - sin^2 x with 1 - sin^2 x we get: cos2x = 1 - 2 sin^2 x.Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.Explanation: One way to simplify this is to use the identity. sin2x +cos2x = 1. From this we can see that. sin2x = 1 − cos2x. Therefore we have. cos2x 1 − cos2x = cos2x sin2x = cot2x. Answer link.How do you differentiate #1+cos^2(x)#? Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer Jim G.Evaluate the integral. ∫ ( cos 2 x - 1) ( cos 2 x + 1) d x. = – ∫ ( 2 sin 2 x) ( 2 cos 2 x) d x = – ∫ tan 2 x d x = ∫ ( 1 – s e c 2 x) d x = x – tan x + C.Feb 17, 2016 · x_1=pi/4 and x_2=(3pi)/4 First, take the half over to the other side to get: cos^2(x) =1/2 then square root: cos(x)=1/sqrt(2). We now need to find the inverse of this. If we look at the graph of cos(x) over the given region we see: graph{cos(x) [-0.1,6.15,-1.2,1.2]} We should expect two answers. 1/sqrt(2) is the exact value for cos(pi/4) So we know at least x_1 = cos^-1(1/sqrt2) ->x_1=pi/4 ... sin(2X) = 2 sinX cosX cos(2X) = 1 - 2sin 2 X = 2cos 2 X - 1 tan(2X) = 2tanX / [ 1 - tan 2 X ] Multiple Angle Formulas sin(3X) = 3sinX - 4sin 3 X cos(3X) = 4cos 3 X - 3cosX sin(4X) = 4sinXcosX - 8sin 3 XcosX cos(4X) = 8cos 4 X - 8cos 2 X + 1Jun 25, 2018 · How do you differentiate #1+cos^2(x)#? Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer Jim G. cos(2x) = cos 2 (x) − sin 2 (x) = 1 − 2 sin 2 (x) = 2 cos 2 (x) − 1 Half-Angle Identities The above identities can be re-stated by squaring each side and doubling all of the angle measures.In this video I will prove cos^2(x)=(1+cos2x)/2. Course Index. What Is The Unit Circle? The Unit Circle and The Angle (Part 1 of 2) The Unit Circle and The Angle ... d^20/dx^20(2cosx cos3x)= A. 2^20(cos2x – 2^20 cos 4x) B. 2^20(cos2x + 2^20 cos 4x) C. 2^20(sin2x – 2^20 sin 4x) D. 2^20(sin2x – 2^20 sin 4x) asked Apr 15, 2021 in Derivatives by Ichha ( 2.7k points)今回は\(\displaystyle\int \displaystyle \frac{1}{\cos^2 x} dx\)を積分していきます。置換積分法を使ったテクニックと微分を使って、下記の積分を実施します。To solve a trigonometric simplify the equation using trigonometric identities. Then, write the equation in a standard form, and isolate the variable using algebraic manipulation to solve for the variable. Use inverse trigonometric functions to find the solutions, and check for extraneous solutions.The angle in the one minus cos double angle trigonometric identity can be denoted by any symbol. Hence, it also is popularly written in two distinct forms. ( 1). 1 − cos ( 2 x) = 2 sin 2 x. ( 2). 1 − cos ( 2 A) = 2 sin 2 A. In this way, the one minus cosine of double angle formula can be expressed in terms of any symbol.Free trigonometric identity calculator - verify trigonometric identities step-by-stepWe would like to show you a description here but the site won’t allow us.Explanation for correct option: Find the value of lim x → 2 1 - cos 2 x - 2 x - 2. Consider the given Equation as. I = lim x → 2 1 - cos 2 x - 2 x - 2. We know that. cos 2 θ = 1 - 2 sin 2 θ. Then, on substituting we have, I = lim x → 2 1 - 1 - 2 sin 2 x - 2 x - 2 ⇒ I = lim x → 2 2 sin 2 x - 2 x - 2 ⇒ I = lim x → 2 2 sin x - 2 x ...sin^2(theta) + cos^2(theta) = 1 (Pythagorean theorem) So 1-cos^2(theta) = sin^2(theta)This simplifies to sinx. Use sin^2theta + cos^2theta = 1 -> sin^2theta = 1- cos^2theta and csctheta = 1/sintheta. =(sin^2x)(cscx) = (sin^2x)(1/sinx) = sinx Hopefully this helps!In trigonometry formulas, we will learn all the basic formulas based on trigonometry ratios (sin,cos, tan) and identities as per Class 10, 11 and 12 syllabi. Also, find the downloadable PDF of trigonometric formulas at BYJU'S. This simplifies to sinx. Use sin^2theta + cos^2theta = 1 -> sin^2theta = 1- cos^2theta and csctheta = 1/sintheta. =(sin^2x)(cscx) = (sin^2x)(1/sinx) = sinx Hopefully this helps!Jan 23, 2017 · 🏼 https://integralsforyou.com - Integral of 1/(1+cos^2(x)) - How to integrate it step by step using the substitution method!🙈 𝐒𝐚𝐦𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥, ?... 1 Answer. George C. Nov 15, 2015. Use cos2x +sin2x = 1 to find: 1 − cos2x sinx = sinx.It is indeed true that sin2(x)= 1 −cos2(x) and that sin2(x)= 21−cos(2x). How do you use the half-angle identities to find all solutions on the interval [0,2pi) for the equation sin2x = cos2(2x) ? 3π,π and 3.5π Explanation: Use cos2a = 2cos2a−1 . The given equation is sin2x = 1−cos2x = 1−(2cos2(2x)−1)2 = cos2(2x) ...Teks video. 1 Min Cos 2 X per 1 + cos 2x = sebelum kita kerjakan soal berikut perlu kita ingat kembali bahwa cos 2x kita bisa berubah menjadi 1 min 2 Sin kuadrat X sehingga 1 Min Cos 2 e-paper 1 + cos 2x bisa kita rubah menjadi 1 Min cos 2x nya kita bahas 1 min 2 Sin kuadrat X per 1 + cos 2x ditambah 1 Min Sin kuadrat X kemudian 1 dikurang 1 habis kemudian Min ketemu Min jadinya + 2 SinX per 1 ...Trigonometry. Simplify square root of 1-cos (x)^2. √1 − cos2 (x) 1 - cos 2 ( x) Apply pythagorean identity. √sin2(x) sin 2 ( x) Pull terms out from under the radical, assuming positive real numbers.Sep 13, 2016 · cos x Use trig identity: cos 2a = 2cos^2 a - 1 We get: 2cos^2 (x/2) - 1 = cos x. Trigonometry . Science Anatomy & Physiology Astronomy ... Trigonometry. Solve for ? cos (x)=-1/2. cos (x) = − 1 2 cos ( x) = - 1 2. Take the inverse cosine of both sides of the equation to extract x x from inside the cosine. x = arccos(−1 2) x = arccos ( - 1 2) Simplify the right side. Tap for more steps... x = 2π 3 x = 2 π 3. The cosine function is negative in the second and third quadrants.You don't have to memorize all formulas but it helps to do so. If you remember, 1 = cos^2 x + sin^2 x. So we have, cos^2 x = 1 - sin^2 x and sin^2 x = 1 - cos^2 x. If we replace cos^2 x in the first double angle formula cos2x = cos^2 x - sin^2 x with 1 - sin^2 x we get: cos2x = 1 - 2 sin^2 x. simplify\:\tan^4(x)+2\tan^2(x)+1; simplify\:\tan^2(x)\cos^2(x)+\cot^2(x)\sin^2(x) Show More; Description. Simplify trigonometric expressions to their simplest form ...The first step is to multiply the two expressions between parentheses : (II) There is a trigonometric identity that states : Working with this expression : ⇒. (I) Using the equation (I) in (II) : ⇒. arrow right.Trigonometry. Solve for x cos (2x)=-1. cos (2x) = −1 cos ( 2 x) = - 1. Take the inverse cosine of both sides of the equation to extract x x from inside the cosine. 2x = arccos(−1) 2 x = arccos ( - 1) Simplify the right side. Tap for more steps... 2x = π 2 x = π. Divide each term in 2x = π 2 x = π by 2 2 and simplify.Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Simplify and combine like terms. Tap for more steps... 1−2cos(2x)+cos2(2x) 1 - 2 cos ( 2 x) + cos 2 ( 2 x)You don't have to memorize all formulas but it helps to do so. If you remember, 1 = cos^2 x + sin^2 x. So we have, cos^2 x = 1 - sin^2 x and sin^2 x = 1 - cos^2 x. If we replace cos^2 x in the first double angle formula cos2x = cos^2 x - sin^2 x with 1 - sin^2 x we get: cos2x = 1 - 2 sin^2 x.
Precalculus. Solve for ? cos (x)^2-1=0. cos2 (x) − 1 = 0 cos 2 ( x) - 1 = 0. Add 1 1 to both sides of the equation. cos2(x) = 1 cos 2 ( x) = 1. Take the specified root of both sides of the equation to eliminate the exponent on the left side. cos(x) = ±√1 cos ( x) = ± 1. Any root of 1 1 is 1 1. cos(x) = ±1 cos ( x) = ± 1.. Cheap sectional sofas under dollar400
1. I'm being asked to find the arc length of y = sin(x) y = sin ( x) for [0, π 2] [ 0, π 2] using M8 M 8. I've determined that y′2 =cos2 x y ′ 2 = cos 2 x. So, using the formula for arc length, I get 1 +cos2 x− −−−−−−−√ 1 + cos 2 x as my function. Now, they want me to evaluate this using M8 M 8, so I end up with 8 8 ...The expression 1 + cos 2x + cos 4x + cos 6x is equivalent to. NCERT Solutions. NCERT Solutions For Class 12. NCERT Solutions For Class 12 Physicsx_1=pi/4 and x_2=(3pi)/4 First, take the half over to the other side to get: cos^2(x) =1/2 then square root: cos(x)=1/sqrt(2). We now need to find the inverse of this. If we look at the graph of cos(x) over the given region we see: graph{cos(x) [-0.1,6.15,-1.2,1.2]} We should expect two answers. 1/sqrt(2) is the exact value for cos(pi/4) So we know at least x_1 = cos^-1(1/sqrt2) ->x_1=pi/4 ...You don't have to memorize all formulas but it helps to do so. If you remember, 1 = cos^2 x + sin^2 x. So we have, cos^2 x = 1 - sin^2 x and sin^2 x = 1 - cos^2 x. If we replace cos^2 x in the first double angle formula cos2x = cos^2 x - sin^2 x with 1 - sin^2 x we get: cos2x = 1 - 2 sin^2 x. Proof cos^2 (x)= (1+cos2x)/2. Proof Half Angle Formula: sin (x/2) Proof Half Angle Formula: cos (x/2) Proof Half Angle Formula: tan (x/2) Product to Sum Formula 1. Product to Sum Formula 2. Sum to Product Formula 1.Ratnaker Mehta. Sep 2, 2016. ∫ 1 (cosx)2 dx = ∫sec2xdx = tanx + C. Answer link.Mar 12, 2018 · Explanation: 1 cos2x − 1 = 1 − cos2x cos2x = sin2x cos2x = tan2x. Answer link. Using #color(blue)" Double angle formula "# #• cos2x = cos^2 x - sin^2 x# and the identity # cos^2x = 1 - sin^2x #. #rArrcos2x = cos^2x - sin^2x = (1-sin^2x) - sin^2x # ...🏼 https://integralsforyou.com - Integral of 1/cos^2(x) - How to integrate it step by step using integration by substitution!🚶 𝐒𝐭𝐞𝐩𝐬00:00 Substitution...Feb 17, 2016 · x_1=pi/4 and x_2=(3pi)/4 First, take the half over to the other side to get: cos^2(x) =1/2 then square root: cos(x)=1/sqrt(2). We now need to find the inverse of this. If we look at the graph of cos(x) over the given region we see: graph{cos(x) [-0.1,6.15,-1.2,1.2]} We should expect two answers. 1/sqrt(2) is the exact value for cos(pi/4) So we know at least x_1 = cos^-1(1/sqrt2) ->x_1=pi/4 ... Explanation: (1) Use the trigonometric formula, cos (a + b) = cos a cos b – sin a sin b and substitute a = b = x. Now write cos 2 x + sin 2 x for 1 on the right side of the equation, (2) Multiply the equation cos2x = cos 2 x - sin 2 x by negative 1 and add 1 on both sides. 1. Yes, cos2(x) cos 2 ( x) usually means cos(x) ⋅ cos(x) cos ( x) ⋅ cos ( x). Most other information already given here is also correct: cos2 x cos 2. . x is probably most common as shortest. (cos(x))2 ( cos. . ( x)) 2 is most clear for beginners, but not practical - it has too much brackets, that are annoying to write and obscure ... .