(iii) Use De Moivre's Theorem to show that cos 40 = 8 cos 0-8 cos0 + 1. (iv) Hence, find all the roots to the equation 16x*- 16x2 + 1 = 0. (v) Hence or otherwise, deduce that: 5Tt cos- 120 cos- 12 4

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A: We have to find theta

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A: To solve the following trigonometric equation  2sin2x - cosx = 1

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A:

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A: Since you have asked multiple questions in single request  so we  will be answering only first…

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A:

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A: To prove that the distance of the roots of the equation…

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A:

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A: The given equation 8x3-4x2-4x+1=0 Roots of the equation are cosπ7, cos3π7, cos5π7 use trigonometric…

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A:

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A:

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A: Given,  2 sin(θ)=2

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A:

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A: Here we solve inverse trigonometry problem.

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A:

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A:

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A: given :

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A: Given equation, cos4α-cos2α=sin(5α)

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A: Given,

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A:

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A:

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A:

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A:

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A:

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A:

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A: The given trigonometric expression is, 4sin2x+3cos2x=5432+42sin2x+332+42cos2x=545sin2x+35cos2x⋯⋯1…

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A: Explanation and solutions is given below.....

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A: Our objective is to find theta.

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A: Solve : -5cos2Bcos6B Use formula = [cos(a-b)+cos(a+b)]/2

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A:

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A:

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A:

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A: See the details solution in below

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A:

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A: A detailed solution is given below.

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A: follow 2nd step

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A: 1. The given equation is 2tan2t=3sect. Solve the above equation as follows.

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A: cos 3x = -cos 6x

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A: 15(a) The left side is cos 3θ=cos 2θ+θ=cos 2θ cos θ-sin (2θ) sin θ=cos2 θ -sin2 (θ) cos θ-2 sin (θ)…

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A:

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A:

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

A:

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A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

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A:

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A:

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A:

Q: V125 cos- - j sin 11 11 1. Simplify . Express answer in rectangular form. 4т + j sin 5 cos- 11 - 11…

A: As per the guidelines, I am supposed to do the first 3 questions only. Kindly repost the other…

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A: Here we will solve for θ,