21 Prove the identity.cos x (1 ²x) 2 2. - sin sec X,

Q: 2. Prove the identity: (cos x- sin x)2 + (cos x + sin x)2 = 2. %3D

A: To prove  that cosx-sinx2+cosx+sinx2=2

Q: Prove the identity. cos(x-y) / cosx cosy = 1+tanx tany

A: To Prove:cosx-ycosxcosy=1+tanxtany

Q: 11. Prove the identity sin x 1+ cos x 2 csc x 1+ cos x sin x

A:

Q: 2. Prove the following identity: sin (x+y)sin (x-y)=cos² y-cos²x X =COS - COS¯ x X.

A:

Q: Locate and identify the absolute extreme values of a. ln (cos x) on [-pai/4, pai/3], b. cos (ln x)…

A: a.Given:

Q: 47' sin z = x³ . cos z + sin z - 3z² Select one: True False

A: Given that d(x3 sinx)/dx  . Here we derivative of this question with respect to x. We know that…

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

A:

Q: 3 sin° x -dx Evaluate ' cos° x

A:

Q: Prove the identity. 3. cos X sim x= 2. S1in X-Sin x) COSX

A:

Q: 5. Verify the identity: sin(x- y)cos y+cos(x– y)sin y = sin x

A: Explanation of the solution is given below.....

Q: 36. (a) Prove the reduction formula 1 cos"-'x sin x + п S cos"x dx = | cos"-2x dx n n (b) Use part…

A:

Q: 2 cos" (x)–sin°(z)+1 cos(x) 3 cos(x) 10. Verify the following identity, justifying each step.

A:

Q: snip

A: Our Aim is to establish the identity given below:-1-sinθcos (θ)=cos (θ)1+sinθ-(i)

Q: Verify the identity: cos(3x) cos(x)(1 – 4 sin? (x))

A: we have to verify the given identity. the solution is following

Q: (14) Prove the following identity cos(x + y) + cos(x - y) = 2 cos(x) cos(y). Make sure you show all…

A: We have to prove the given identity- cos(x + y )+cos(x - y) =2cos(x) cos(y).

Q: Evaluate (cos x In sin x) dx. Select the correct response: O cos x (In sin x-1) +C sin x (In cos…

A:

Q: III. Verify the identity. 5.) 1-Cos 2x tan?x %3D 1+ cos 2x

A:

Q: 12. Evaluate Cos 0 -sin & - Bin sin 0 Co3 0

A: Given: cosθ−sinθsinθcosθ4

Q: Verify the identity. 2 sin(x) cos(x) = 1 (sin(x) + cos(x))2 - 1

A:

Q: Q4: Prove that: cos?x – sin?x cos²x - 1- tan?x

A: We need to prove that cos2x-sin2xcos2x=1-tan2x We will use tanx =sin xcos x

Q: 3 3. Find the value of cos(2x) given that sin x = -and x is in QII.

A:

Q: 4. Prove the identity csc 0 – sin 0 = cot 0 cos 0.

A:

Q: Verify the identity. 6 cos(sin-1 x) = / 36 – 36x2 Let 0 = sin-1 x = sin 0 = x = X. Thus, 6 cos(sin-1…

A: use trigonometric identity  to verify it.

Q: VII. Prove the following identities. tan x-cot x sin' 0+cos' 0 =1-2cos x =1-sin@cose 11. 20. tan…

A:

Q: 2. Prove the identity: cos (x-y)– cos (x+y) = 2 sinx siny

A:

Q: 25л then 6. If 0 sin(0) - cos(0) =

A:

Q: 16. Establish the identity: os 0)² + (sin 0- cos 0)2 = 2 %3D

A: We need to establish the identity  (sinθ+cosθ)2+(sinθ-cosθ)2=2

Q: 1) Prove that cos°(x) + sin (x) = 1. (refer to notes). Use the "Square" formula.

A: See the attachment

Q: 1) Using the formula: cos(x + y) = cos x cos y - sin x sin y, prove in steps that: cos? x = 1+cos 2…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 1) Using the formula: cos(x +y) = cos x cos y - sin x sin y, prove in steps that: cos? x = %3D 1+cos…

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Q: 7. Prove the following identities. sin x 1 + cosx 1- cos x a. 1-cos x b. 1 + cos x tan? %3D sin x II

A:

Q: 1) Using the formula: cos(x +y) = cos x cos y – sin x sin y, prove in steps that: cos? x = 1+cos 2 x

A:

Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x

Q: 4. Establish the identity using the sum and difference formulas: sin (m – 0) = sin 0

A:

Q: 24. Prove the identity 1 – (sin x – cos x)2 = sin 2x

A:

Q: 5. Prove the identity. csc 0- cot 0 sin- 2 2 csc e

A:

Q: Simplify sin “ z – cos“ æ O 2cos (x) - 1 O 2sin*(x) - 1 O 1+ 2sin*(x) O 1+ 2cos (x)

A: Using trigonometric identities.

Q: 7. Prove the identity. 1-cos 20 tan 0 %3D sin 20

A:

Q: 40. Verify the following identities. a) sin (2r) = tan x (1 + cos (2x)) cof (20)3극(cot0-tan e) b)…

A: sin2x=tanx(1+cos2x)we know that…

Q: Which of the following is equivalent to [sin(-x) + cos(-x)]? 1 - 2sinxcosx O 1 O 1+ 2sinxcosx O…

A: Use Trigonometric identities and simplify.

Q: Verify the identity: [cos(x + h) - cos x]/h = cos x. (cos h - 1)/h - sin x. (sin h)/h

A: we have to verify the identity : cos(x+h)-cosxh=cosx(cosh-1)h-sinx(sinh)h

Q: 1) Using the formula: cos(x + y) = cos x cos y – sin x sin y, prove in steps that: cos? x = %3D…

A: Note - Since you have posted multiple questions, I am answering first one for you as per the…

Q: 5. Prove the following Identity: sin(2x) 1+ cos(2x) tan(x)

A: Use the following identities to prove  the given  identity. sin²x+cos²x=1 cos(2x)=cos²x-sin²x

Q: 4. Verify the identity: 1 cos(x)+1 1 + cos(x)-1 -2 csc(x) cot(x)

A:

Q: 1- cos 0 1+ cos 0 sin 0

A:

Q: x) - 0.5 cos(x)) on the

A: Given as, f(x)=e-x3.2sinx-0.5cosx in the interval [3, 4].

Q: 7. Prove the identity. – sin 3 TT -x= 0 2 sin +x 2

A:

Q: |(1+ sin x)'cos x in x) cos x cOS.

A: Given: ∫1+sinx3cosxdx

Q: Verify the identity. (1 – cos"(x)(1 + cot*«») = (1 - cos (x)(1 + cot°») - sin°C«) - 1 + sin (x) =…

A: Solved below

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.