Question

SinA-2Sin^3A/2Cos^3A-CosA=tanA
Prove that :

SinA (1-2sin^2A)

Answer 1

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Answer 2

$\frac{sina - 2 {sin}^{3} a}{2 {cos}^{3} a - cosa} \\ \\ = \frac{sina(1 - 2 {sin}^{2} a)}{cosa(2 {cos}^{2}a - 1) } \\ \\ = \frac{sina(cos2a)}{cosa(cos2a)} \\ \\ = \frac{sina}{cosa} \\ \\ = tana$