5. Find the solution(s), if any, of the following equations. (a) cos (2x) = 5 cos(x) + 2, where a E [0, 27). %3D (b) (-VF+1)- '(-Vx² +1) – tan-(t/3) = cos '(1). CsC

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A: Derivative of function

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A:

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A:

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A:

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A: This question can be solved by applying the concepts of integration of trigonometric functions.

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A: Given,

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A:

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A:

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A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

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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: Given, hx=lncosx+kx We have to find the value of k for which h'π4=6

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A:

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A:

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A:

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A: Given f"(x)=-9sin(3x) and f'(0)=-6 and f(0)=3

Q: Q2: Find General Solution (YGS)to the equation (Yª-1) Y=COS(2x)

A: From the given information. The given differential equation is as follows.