8. Verify the identity: 1- cos h sin? h h h(1 + cos h)

Q: Prove the identity. +x + sin 6. sin = cos x

A: Given, We have to prove the identity sinπ6+x+sinπ6-x=cosx

Q: 1-cos . Fill in the blank: sin(_) = V 2 O 7y

A: As per our guidelines we are only supposed to solve first question in case of multiple questions

Q: 6. Use Euler's Formula to prove the following identities: eio terio cos O ei0 -e-i0 %3D and sin 0 =…

A: We have by Euler's formula, eiθ=cosθ+isinθ.....1e-iθ=cosθ-isinθ....2 Then adding equation (1) and…

Q: Given that cos(x) = 0.42, what is cos(-x)?

A:

Q: Verify the identity: cos A sin' A 1 %3D 1 – cos A -

A:

Q: Prove the following identities: sin 6+ sec 0) +(cos 0+ sece) = (1+sec0 cosece)

A: We can easily prove this given identity shown below

Q: 3. Which is equal to (sin a + cos a) +(sin r cos a) using identities? CO O 2 -2 О-1

A:

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

A:

Q: .

A: The given matrix is,

Q: 2. To create an identity for the equation cos x( 1+cotx) = A, where A would need to be A. cos'x B.…

A:

Q: cos(x + y) cos(x – y) = cos? (x) – sin²(y)

A:

Q: 1, Solve for o 0-2T (a) sine 2 W cos 28 = 8- %3D O Zsin e- =o - omis ce)

A:

Q: sin² e – cos e tan 0- cot e = sin e cos e

A: A) sin2θ-cos2θsin θ cosθ=sin2θsin θ cosθ-cos2θsin θ cosθ=sin θ cosθ-cos θsin θ =tan θ- cot θ

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: Determine the following: a) sin^-1(√2/2) b) cos^-1(-√2/2) c) cos^-1(tan(π/4)) d)…

A: Solution of the problem as follows

Q: The value of the expression cos z - tan z – 9+ sin z+ secz is

A: given expression is…

Q: ve the following identities! no tan 0 sec 0 cosec e cos e 1+cos e

A: Please refer to the image below

Q: 3. Using the fact that sin 2a = 2 sin a cos a, and the fact that 0 = 2a, rewrite the area of the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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: 14. Find the exact value of sin(-) if cos(r) 1 and 270° < x << 340°. ii) ii) - 2 iv) not listed

A:

Q: Q2-By using the formula cos(A – B) = cosAcosB + sinAsinB & sin(A – B) = sinAcosB - cosAsinB…

A:

Q: Prove: sin? x 2 cos“ = cos 2-2cos x

A: We will use basic properties of trigonometric ratios

Q: Prove the identity on a separate sheet of paper. tan 6+ sin e cos 2 tan e

A: In this question we have to prove the following identity.

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: Give the exact value of COS (-) + sin ( 3 V3 O1 2 2 O V2 O 1+v3

A: We need to find the exact value of the given trigonometric ratios.

Q: Verify the following identities. 1 (1- cose)(1+ cos 0)= csc? 0 2 а. sine(tane + cote)= sec e b.

A:

Q: 1. Verify that the following equations are the identity csc2 (-x) tan(x) cot(-a) - sec2 (r) a. %3D |

A: Given problem:-

Q: 2-Find O for: y3tan? (cos x).

A: Using Chain rule we can solve the given derivative problem

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: Evaluate 3 cos z sin" e dz.

A:

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

A:

Q: Prove the following identity. sin 20 cot 0 = 1 - cos 20

A: givencotθ=sin2θ1-cos2θwe know double angle formulasin2θ=2sinθcosθcos2θ=1-2sin2θlet us consider right…

Q: 4. Verify the following identities: a. sin 3x = 3 sin x-4 sin3 x b. 1+ cos 10x = 2 cos? 5x %3D

A:

Q: 4. Prove the following identity: 1 - tan?a cos2a %3D sec?a Sin(420) b sin7d

A:

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

A: Given,          cosx+ycosx-y=cos2x-sin2y

Q: Prove that, cos20 + sin?0 = 1

A: Let a, b and c be the lengths of right angled triangle. Then by definition,

Q: Q2-By using the formula cos(A – B) = cosAcosB + sinAsinB & %3D sin(A – B) = sinAcosB- cosAsinB…

A:

Q: Q1- Show that cote)+tan(e) a. cofe)-tan(9) sec(20) b. sin(36) = 3 sin(@) - 4sin (0) = Se %3D

A:

Q: ди du and ar if u = e" cos 0 . cos(r sin 0) (1) Find

A: It is partial derivative

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

A: The given function is z=sinx2 cosy2.

Q: (9) Verify the following (a) cos e + sin 0 tan e = sec e %3D

A: As per guidelines we can answer only one question at a time, so if you need more answer kindly…

Q: Verify the trigonometric identity sin(z - 1/2) = - cos(z)

A:

Q: – 57 then - If 0 : sin(0) = cos(0) = COS %3D

A: Given : θ = -5π/6 Then, sinθ = sin(-5π/6) = sin(-5×180/6) sin(-150) = -sin(150)         [∴ sin(-θ)=…

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.

Q: 12. Verify the following trigonometric identities. tan (x) sin (2x) = 2 – 2 cos (x)

A: To verify the identity: tan(x)sin(2x)=2-2cos2(x) Solution: We know, tan(θ)=sin(θ)cos(θ)…

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

A: