EXAMPLE 5 Prove cos 4x = 8 cos“ x – 8 cos? x + 1. PROOF We can write cos 4x as cos (2 · 2x) and apply our double-angle for- mula. Because the right side is written in terms of cos x only, we will choose the second form of our double-angle formula for cos 2A. = cos (2 · 2x) = 2 cos 2x – 1 = 2(2 cos? x – 1)² – 1 = 2(4 cos* x – 4 cos? x + 1) – 1 = 8 cos x - 8 cos x + 2 – 1 = 8 cos“ x – 8 cos? x + 1 cos 4x Double-angle formula Double-angle formula %3D Square || Distribute Simplify |

Q: Verify the identity. (7 cos x-4 sin x)2 + (4 cosx+7 sin x)2 = 65

A: Given,           7cosx-4sinx2+4cosx+7sinx2=65

Q: 3(sin^2 90degrees-2sin 90degrees cos 90degrees+ cos^2 90 degrees)

A:

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

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Q: Find the value of 2 32 tim (22 (1 - cos (2) - cos (4) + cos (2) cos (=))} x →0 8 X

A: Sol:- limx→032x81-cosx22-cosx24+cosx22cosx24Expand…

Q: Find the value of cos 1° + cos 3° + Cos 5° +... + cos 177° + cos 179°

A: We can solve this as follows:

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

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Q: 1. Let 57 < A< 6n. Then tan 4 is negative. 2. Let 27 <0 < 37. Then cos 1+cos @

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Q: find the value of sin^2(21degrees)+cos^2(21 degrees) - sin(70degrees)/cos(20degrees

A: the value of sin^2(21degrees)+cos^2(21 degrees) - sin(70degrees)/cos(20degrees

Q: (cos 20+5 sin 20) (cos 30 + i sin 30) 2. (cos 40 i sin 40)(cos 66+i sin 60) 1/3

A: We know, from De moiver's theorem,  ( cosθ + i sinθ )n = ( cos nθ + i sin nθ)

Q: 7. Prove the identity. 1- cos x = (cscx- cotx)? 1+ cos x To verify the identity, work each side…

A: we have to rove the identity1-cos x1+cos x=(cosec x-cot x)2 taking left hand side 1-cos x1+cos…

Q: cos-1(cos(5π/3))

A:

Q: 5. cos() 7. 6. cos(3) 8. cos(2)

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Q: 1. [4(cos 12° + i sin 12°)]³. 3. [√3 (cos 25° + i sin 25°)].

A:

Q: 3 5 -1 cos sin cos 5 13

A:

Q: snip

A: sin4θ=sin2θ2=1-cos2θ22=141+cos22θ-2cos2θ=141+1+cos4θ2-2cos2θ=14+1+cos4θ8-12cos2θ=14+18+18cos4θ-12cos…

Q: 3. sin 27° =cos ? cos 73° cos 153° cos 27° cos 63° O O O O

A: To find equivalent of sin27

Q: Circle any expression below equivalent to sec (2.5) - 1 cos cos(2.5) 1 cos 2.5 cos(2.5) 2.5 None of…

A: sec-12.5

Q: Verify the identity 2 sin3θ cos θ + 2 sin θ cos3θ= sin 2θ.

A:

Q: Establish the identity cos ²(80) – sin2(80) = cos (160).

A: Given : cos28θ - sin28θ = cos16θ

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: Establish each identity.

A: Solution:To establish1+cos 2θ+cos 4θ+cos 6θ=4 cos θ cos 2θ cos 3θFormula:cos A + cos B= 2 cos A+B2…

Q: Find sin 0 and cos 0 if tan 0 sin = 3/5 sin = -3/5 sin = 4/5 sin = -4/5 cos = 3/5 cos = -3/5 cos =…

A:

Q: 3. The values of cos 30 can be obtained by using the expression for cos( 0 + B). Elaborate your…

A:

Q: Establish each identity.

A: Our Aim is to prove the identity given below:-1-cos 2θ +cos (4θ)-cos (6θ)=4 sin (θ) cos (2θ) sin…

Q: Find sinθ and tan⁡θ if cosθ=11/61 assuming that 0≤θ<π/2 sinθ= tanθ=

A: Given,          cosθ=1161 ; 0≤θ&lt;π2

Q: snip

A: cos1°+cos2°+cos3°+---+cos358°+cos359°

Q: 50. cos(27-0) = cos 0

A:

Q: (a) Is it true that cos (2 - 30°) = 2 cos 30°? Give exact answers in simplest form. (b) Expand cos…

A:

Q: Find the exact value of the expression. 9. 8 sin sin ~1 cos 41 17 8 sin sin -1 Cos - 41 17

A: Question is solved.

Q: Verify the identity: 2 sin3 θ cos θ + 2 sin θ cos3 θ = sin 2θ

A: Verify the identity: 2 sin3 θ cos θ + 2 sin θ cos3 θ = sin 2θ

Q: 13 7. tan | sec 5. -1 4 8. sin cos I5 9. sin (sin n) 10. csc (sec '2)+ cos (tan 3

A: NOTE: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Example 4: Suppose that sin a = 0.32. What is the value of cos(90-a)? Explain.

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Q: sen? 2. a + COS cos a-1

A: We know that,   tanθ = 1/cotθ    sen2α  =  1 - cos2α

Q: If x + = 2 cose X then show that 1 = 2 cos 20 X* + X

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Q: 5) 2√√3 cos sin 0 - cos 0 = 2cos 0

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

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Q: 2. Ifsin 60° , and cos B find ß. Explain. %3D 2 2

A:

Q: 17 7) cos 8) cos -810 9 9) cos 15x 10) sin 4. 11) sin 12) tan -945o

A:

Q: Evaluate the expression cos−1(sin(3π4))

A:

Q: cos(50) – cos(70) = 0

A: Given: To solve cos5θ-cos7θ=0 From the given equation, a=5θb=7θ

Q: 9 (cos 20° + i sin 20°) · 4 (cos 113° + i sin 113°) Leave your final answer in Trig Form.

A: The sum rule of cos and sin are: cos(A-B)=cosAcosB+sinAsinBsin(A+B)=sinAcosB+sinBcosA The given…

Q: (A[cos(6) - 3 cos(3) + 2] + B[– sin(6) +3 sin(3)] = 2, A[sin(6) + 3 sin(3)] + B[cos(6) – 3 cos(3) +…

A: Given that, Acos6-3cos3+2+B-sin6+3sin3sin3k+Asin6-3sin3+Bcos6-3cos3+2cos3k=2sin3k

Q: cos 70 +i sin 70 b). cos 20-isin 20

A:

Q: cos 2(theta) if sin theta = 5/8

A: Here we have to find cosθ2 and cos2θ=? If sinθ=58 where 0≤θ≤π2

Q: 18. Prove tan (0)+1= sec (0) 19. Solve: 2cos? (3x) + 5cos (3x)- 3 = 0 a. b. 4 cos

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Q: how can 2sin(2β)cos(4β) be expressed as a sum?

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Q: (a) Is it true that cos (2-45°) = 2 cos 45°? Give exact answers in simplest form. (b) Expand cos…

A: Introduction: The sine function, cosine function, and tangent function are among the six primary sum…