Show that sin (A + B) + sin (A – B) = 2 sin A cos B. -

Q: 2 v sec 2 1+ cos 0°

A: We have to find the identity

Q: snip

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Q: Show that A" cos (ах ah + b) = | 2 sin cos a + bx +n (ah + T 2

A:

Q: Find the exact value of cos2 15° - sin2 15°.

A: We have to find the exact value of cos2 15°-sin2 15°Formula used :-Cos 2θ= cos2 θ-sin2θ -1

Q: Verify that if y = ƒ(θ2 sin θ, then y'(θ) = ƒ'(θ) sin θ + ƒ(θ) cos θ.

A: We use the product rule

Q: Assume that sin u = 3/5 and sin v = 4/5. Find cos (u - v). I need all work.

A: Given:

Q: tan 0 de equals to : 1+sece In |1+tane|+c In |1+sece|+c O (tane)^2/2+c -In |1+cose|+c

A:

Q: ) Prove that 2+sinZA Cos A-SinA

A: To Prove: cos3A-sin3AcosA-sinA=2+sin2A2

Q: 2) VERIFY THE IDENTITY sin +0 =-cos 0. 2.

A: We need to verify the identity.

Q: PROVE that sin x = V1 – cos² x is NOT an identity. -

A:

Q: x+(1/x)=2 cos theta , then show that x2+(1/x2 )=2 cos2 theta

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Q: Express the 10th term of ( x1 + x2)º in terms of sinusoidal functions (sin, cos).

A: The expression is x1+x220. As we have obtained…

Q: Prove the identity: cos(x + y)cos(x – y) = cos?x – sin²y

A:

Q: 2+7 sin cos z zp-

A: Given: ∫2+7sin3zcos2zdz

Q: snip

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

Q: cos 2x +1 Prove that sin 2x

A:

Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

A:

Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: Use De Moivre's Theorem with n= 3 to express cos 3θ and sin 3θ in terms of cos θ and sin θ.

A:

Q: Use the Intermediate Value Theorem to prove that sin x − cos x = 3x has a solution, and use Rolle’s…

A:

Q: /2 sin aVT-2 cos r dr /3

A: To find the given integration

Q: 6. Prove that: ah cos (i) A sin (ar + b) = 2 sin (ah sin a (ii) A cos (ar + b) = - 2 sin

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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: Answer in term of "u" : cos(sin^(-1)(u))

A:

Q: Rewrite cos x+ in terms of sin(x) and cos(z). 4

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Q: Exercise 3. Show that (a) sin z = sin z: (b) cos z = cos 7.

A:

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

A: In question We have given two identities and we'll prove it, (i). Cos(π + x) = - Cosx  (ii). Cosx…

Q: Q/prove that : (cos x) = -Sin X %3D

A:

Q: Find sin(2x), cos(2x), and tan(2x) from the given tan(x) = -, cos(x) > 0 %3D sin(2x) = %3D cos(2x) =…

A: Given: tanx=-16,   cosx>0 sin2x can be calculated as, sin2x=2tanx1+tan2x          =2×-161+-162…

Q: Verify the identity. cos 2x cos² r - sin? x

A: We have to solve the trigonometry problem

Q: Which is equal to (sin⁡x+cos⁡x)^2+(sin⁡x−cos⁡x)^2 using identities?

A: Now we use identity  Sin2x +cos2x =1 And formula (a+b)2= a2 +b2 + 2ab  (a-b)2 = a2 + b2 - 2ab

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

A: sin t - cos 2t=(2sin t-1)(sin t +1)Formulascos 2t= 1-2sin2t

Q: The integartion of [sin(sinØ)]Ø cos dø Is: cos(sin0)+C -sin(cos Ø) + C O -sin(sinØ) + C O -cos(sinØ)…

A:

Q: Use De Moivre’s Theorem with n = 3 to express cos 3θ and sin 3θ in terms of cos θ and sinθ.

A: To express cos3θ and sin 3θ in terms of cosθ and sinθ, using De Moivre's theorem with n=3. De…

Q: PROVE that sin x = v1 – cos² x is NOT an identity.

A: Topic:- trigonometry

Q: Prove that sin? 0 + cosª 0 = sin“ 0 + cos² 0.

A: Using fundamental identity of trigonometry.

Q: ( esch(3 tan z) + sin². 1. cos? r

A:

Q: Find a series of cosines of multiples of x which will represent (x sinx ) in the interval (O, x) and…

A: Let's expand x cos(x ) , xcosx=x1-x22!+x44!-x66!+...=x-x32!+x54!-x76!+...             in 0,x To show…

Q: у%3D sin(4x — 2) cos (4x + 2) || -

A: topic - derivative

Q: Can the Intermediate Value Theorem be used to prove that the equation 9 2(r + 9) sin*(x) – 4 cos"(x)…

A:

Q: Prove that ²-1 (²) (0) (sin (+,-) + do r² sin(0)

A: Given : ∇2=∂2∂x2+∂2∂y2+∂2∂z2 To Prove : ∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2 sin2θ∂2∂ϕ2

Q: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

Q: Find z where z = sin (æ²) cos (4²) COS

A: The given function is z=sinx2 cosy2.

Q: (3) Prove that Sina cos a -Sinß cos B sin cos B sinß cosy sin(2+ B+y)

A: We have have to solve given problem:

Q: Prove by MSE that a. sin 90° = 1 b. cos 180° = -1

A:

Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.