4 cos[tan"! cos! 3 Find the exact value of 12 13

Q: cos 30° + sin 60° V3 Prove that 1+ cos 60° + sin 30° 2.

A: Given to prove : cos30∘+sin60∘1+cos60∘+sin30∘=32…

Q: Find all solutions to 2 cos(0) - V3 on the interval 0 < 0 < 27. Give your answers as exact values in…

A:

Q: 57 Rewrite cos x - in terms of sin(x) and cos(x). No decimals. 3

A: Here we will use the formula...   Cos (A-B) = Cos A Cos B + SinA  SinB

Q: 60. tan(cos−1 x + 12 ) = √4 − (x + 1)2x + 1

A: Given :  tan(cos- x + 1/2) = √4 - (x +1)2 /x + 1 where, cos- (x + 1/2), cos-θ = Base/Hypotenuse,…

Q: 1- cos 20+ sin 20 Prove tan e. 1+ cos 20+ sin 20

A: We can prove the given statement as below

Q: 11. Prove the identity. sin 6.4 = 3 sin 2.4 – 4sin 24 12. Prove the identity. cos30 = 4cos 0- 3cose

A:

Q: 1 + sin 0 1 + sin 0 1 - sin 0 |cos 6|

A:

Q: Establish each identity given in attachment.

A: Given ln1+cosθ+ln1-cosθ=2lnsinθ

Q: 3.7 O cos ) cos(8-x) cos - cos 3

A:

Q: Verify the identity: 1/(sin θ + cos θ)+1/(sin θ - cos θ) = 2 sin θ/(sin4 θ- cos4 θ)

A:

Q: 25. Verify the identity. cos (-0) 1+sin (-0) sec 0 + tan 0

A: here is the proof

Q: 1 cos²0 1 sin 9 1 tan 8 + tan 8 + || || Trigono 1 sin² 0 cos²0 1 sin cos 0

A:

Q: 71. a. Is it true that sin (2 · 30°) = 2 sin 30°? b. Expand sin(2 · 30°) as sin(30° + 30°) using the…

A: To find sin(2 .30°)=2 sin 30°and Expand sin (30°+30°) using sum formula for sineFormula:sin 2θ =2…

Q: 1. Prove cos 8-sin 8 cos 8 + sin e = sec 28 tan 20.

A:

Q: Verify the identity. 9 cos2 β − 9 sin2 β = 18 cos2 β − 9

A: To verify the given identity.

Q: 12 Prove that sin 80 cos 0-sin 60 cos 30 a. = tan 20 cos 20 cos 0- sin 30 sin 40

A:

Q: Q1. Simplify (cos-isin )² (cos 70+isin 70)-³ (cos 40+ i sin 40)² (cos+ i sin 0)³ using De Movier's…

A:

Q: 7. Consider the identity 2 tan z 1+tan² z= sin(2r). (a) Verify the identity. (b) Find sin (4) if tan…

A:

Q: 2. Express cos(60) in terms of powers of cos only.

A:

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

A:

Q: 3 1 1 Show that sin 0 - cos (20) + cos (40). 8 8

A: To show that: sin4θ=38-12cos(2θ)+18cos(4θ) Solution: Considering LHS: sin4θ On simplifying further…

Q: 7.) tan 0 sin 0 + cos0 = sec 0

A:

Q: 11. Prove the identity. sin 64 = 3 sin 2A – 4sin³ 2.4

A:

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

A: Given: cosθ−sinθsinθcosθ4

Q: snip

A: Use the identity tan x+y=tan x+tan y1-tan x tan y to expand tan 2θ.

Q: Sın 7. os 3x-Cos 72- Sen 3x tan 22 Cos4a+1

A: We use Trigonometry identities  Sin(A+B) = sin(A)cos(B)-cos(A)sin(B) cos(2A) = 2cos2(A)-1 sin(2A)=…

Q: 39. cos (7 + x) 40. sin(27 - x) 41. sin 42. cos + x 2

A:

Q: 1. If tan z = - 0.5 then tan( – æ) - 2. If sin z = 0.5 then sin( – æ) = 3. If cos a = 0.2 then cos(…

A:

Q: (a) (i) Use de Moivre's theorem to express cos 40 and sin 40 in terms of cos 0 and sin 0. 4 tan3 0 4…

A: Expand the expression:  x+iy4=x4+4ix3y-6x2y2-4ixy3+y4=x4-6x2y2+y4+4x3y-4xy3i Set x=cosθ and y=sinθ…

Q: 5л Compute the exact value of tan ( + 4 ). 6.

A:

Q: 5/2 Sin'2 cos3x

A: write ∫sin52xcos3xdx as ∫sin52xcos2xcosxdx. Use the identity sin2x+cos2x=1. So,…

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: 8. Find all 0 such that -180° <0 < 180° and: cos 0 = - b sin 0 = c tan0 = - a d cos 0 = 0.8 e tan 0…

A: we have given -1800≤θ≤1800a. cosθ=-110⇒θ=cos-1(-110)=95.740b. sinθ=45⇒θ=sin-1(45)=53.130c.…

Q: 7. Consider the identity _2 tanr 1+tan z sin(2r). (a) Verify the identity. (b) Find sin (4) if tan…

A:

Q: Prove the identity: sin(0)-co sin (0) +cos (0)–1 cos (8)+1 sin(0)+1 cos(8)

A: On proving this we will get

Q: 5. Prove the following identity 1-cos x tan? 1+ cos x 2. 2.

A:

Q: 8 1 + cos 3 Cos ( sin 5 17

A:

Q: Find the period N of the sequence x(n) = cos 2nn cos 15 + sin sin 8 60 15 120 4

A:

Q: 5) 2√√3 cos sin 0 - cos 0 = 2cos 0

A:

Q: 3 Verify the identity: csc (0) 1-cos2 (0) cos (20) 2 sin(0) + 2tan(0) cos(0) = %3D sin (0)

A:

Q: 7. Verify the identity 1+cos 2x+2sin² x = 2 1 and <θ<π, find sin- 8. Given tan O 3 2 9. Use half…

A: Explained below

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

A:

Q: Find the exact value.. 1. Cos 70°cos40°+sin70°sin40° 2. Sin 7π/12 using the fact the 7π/12= π/3 +π/4

A:

Q: sin 0(3sin? 0+ 4cos? 0) = 3 cos 0 + cos³ 0 4. Prove that tan 0

A:

Q: Prove : sin 3θ = 3 sin θ + 4 sin3 θ

A:

Q: cos 30° + sin 60° V3 Prove that 1+ cos 60° + sin 30°

A: Trignometric ratios are

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

A:

Q: prove it 6. *cos 4x = 1 - 8 sin?x + 8 sintx

A: Prove : cos 4x = 1 - 8 sin2x + 8 sin4x

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.