Question

Prove the given trigonometric question

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Answer 1

Answer:

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Answer 2

$\underline\mathfrak{Answer} \\ LHS = \frac{ \tan(a) }{( \sec {}^{2} (a)) {}^{2} } + \frac{ \cot(a) }{( \cos\sec {}^{2} (a) ) {}^{2} } \\ \\ = \frac{ \frac{ \sin(a) }{ \cos(a) } }{ \frac{1}{ \cos {}^{4} (a) } } + \frac{ \frac{ \cos(a) }{ \sin(a) } }{ \frac{1}{ \sin {}^{4} (a) } } \\ \\ = \sin(a) \cos {}^{3} (a) + \cos(a) \sin {}^{3} (a) \\ = \sin(a) \cos(a) \: \: \: \\ = \sin(a) \cos(a) = RHS \:$