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Question

Prove that: sinA+2sin2A+sin3AcosA+2cos2A+cos3A=tan2A

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Solution

(Sin3A+SinA+2Sin2ACos3A+CosA+2Cos2A)=(2Sin(3A+2A2)Cos(3AA2)+2Sin2A2Cos(3A+A2)Cos(3AA2)+2Cos2A)=(2Sin2ACosA+2Sin2A2Cos2ACosA+2Cos2A)=(2Sin2A[CosA+1]2Cos2A[CosA+1])=tan2A=RHS

Hence proved.


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