sin A−2 sin3A2 cos3A−cos A=

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Question

\frac{sin A - 2 {sin}^{3} A}{2 {cos}^{3} A - cos A} =

Options:

A . secA

B . cotA

C . tanA

D . 1

Answer: Option C
:
C

\frac{sin A - 2 {sin}^{3} A}{2 {cos}^{3} A - c o s A} = \frac{sin A (1 - 2 {sin}^{2} A)}{cos A (2 {cos}^{2} A - 1)}

= \frac{sin A ({sin}^{2} A + {cos}^{2} A - 2 {sin}^{2} A)}{cos A (2 {cos}^{2} A - ({sin}^{2} A + {cos}^{2} A))}

= \frac{sin A ({cos}^{2} A - {sin}^{2} A)}{cos A ({cos}^{2} A - {sin}^{2} A)}

= tan A

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