Question

solve this question ​

Answer 1

$\implies \: \frac{ \sin 3 A}{ \sin \: A } + \frac{ \cos 3A }{ \cos A } \\ \\ \implies \: \frac{3 \sin A\: - 4 \sin {}^{3} A}{ \sin A\: } + \frac{4 \cos {}^{3}A - 3 \cos A}{ \cos A\: } \\ \\ \implies \: \frac{ \cancel{ \sin \: A} \: (3 - 4 \sin {}^{2} A)}{ \cancel{ \sin A\: }} + \frac{ \cancel{ \cos A\: } \: (4 { \cos}^{2}A - 3) }{ \cancel{ \cos A}} \\ \\ \implies \: \cancel{ 3} - 4 { \sin}^{2} A + 4 \cos {}^{2}A \cancel{- 3 } \\ \\ \implies \: 4( { \cos}^{2} A - { \sin}^{2} A) \\ \\ \implies \: 4 \cos \: 2A$

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