Question

Proove.................

Answer 1

Hi...☺

Here is your answer...✌
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$LHS \\ \\ =\frac{ \tan(A ) }{(1 + \tan {}^{2} ( A ) ) {}^{2} } + \frac{ \cot( A ) }{(1 + \cot{}^{2 } ( A ) ) {}^{2} } \\ \\ = \frac{ \frac{ \sin( A) }{ \cos( A ) } }{ (\sec {}^{2} ( A )) {}^{2} } + \frac{ \frac{ \cos( A) }{ \sin( A ) } }{ (\cosec {}^{2} ( A ) ) {}^{2} } \\ \\ = \frac{ \frac{ \sin( A) }{ \cos( A ) } }{ ( \frac{1}{ \cos^{4} ( A ) } ) } + \frac{ \frac{ \cos( A ) }{ \sin( A ) } }{ ( \frac{1}{ { \sin {}^{4} ( A) } } ) } \\ \\ = \sin( A ) \cos {}^{3} ( A) + \cos( A ) \sin {}^{3} ( A) \\ \\ = \sin( A ) \cos( A ) ( \sin{}^{2} ( A ) + \cos {}^{2} ( A) ) \\ \\ = \sin( A ) \cos( A ) \times 1 \\ \\ = \sin( A ) \cos( A) \\\\ = RHS$

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