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Question

Prove that sinA2sin3A2cos3AcosA=tanA

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Solution

sinA2sin3A2cos3AcosA

=sinA(12sin2A)cosA(2cos2A1)

=sinA(sin2A+cos2A2sin2A)cosA(2cos2Asin2Acos2A) ...... [sin²θ+cos²θ=1]

=sinA(cos2Asin2A)cosA(cos2Asin2A)

=sinAcosA

=tanA

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