verify the given identity 87) csc2x = 1/2 cscxsecx 89) cos(x)/(5) = 1 - 2sin2(x)/(10)

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A: We will use product rule of differentiation here

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A: Use following trigonometric identities  1. cscx = 1sinx 2.(csc2x - cot2x) =1

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A: The explanation of the solution is :

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Q: First, recall that sin²2 (0) = 1 - cos² (0). Thus, substitute (1 - cos²(0)) for sin²(0) in the given…

A: Now we know that sin^2(theta)=1-cos^2(theta)

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Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

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Q: Prove that

A: Given:d2ndx2nsinx=-1n sinxd2ndx2ncosx=-1n cosx

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A: y=cos3(x)+1 Subject to x:

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Q: cscx−sinx cos²x CSC X =

A: We need to prove that cscx-sinxcscx=cos2x

Q: Find a formula for cos(tan^−1(7z)) assuming that z < 0. Show all the work.

A: cos(tan-1(7z))

Q: 4) Verify. cos²(x)[1 C. – tan²(x)] = cos(2x)

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Q: Choose the correct answer If f(x)=ln⁡(cos⁡(3x)) , then f"(x) =…  -9 sec2 (3x)  9 cos2 (3x)  9 tan2…

A: Derivative problem....

Q: Prove that, Cosh(A+B) = CoshACoshB + SinhASinhB. Deduce a similar expression for Sinh(A+B)

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Q: To prove cos (-u) csc (-u) tan (-u) = 1, which of the following is correct as a first step? a. cos…

A: cos-u csc-u tan-u=1