Question

tan^2θ/1+tan^2θ + cot^2θ/1+cot^2θ =1

Answer 1

Step-by-step explanation:

$LHS\\\frac{ { \tan( \alpha ) }^{2} }{1 + { \tan( \alpha ) }^{2} } + \frac{ { \cot( \alpha ) }^{2} }{1 + { \cot( \alpha ) }^{2} } \\ \frac{ { \tan( \alpha ) }^{2} }{ { \sec( \alpha ) }^{2} } + \frac{ { \cot( \alpha ) }^{2} }{ { \cosec( \alpha ) }^{2} } \\ { \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} \\ 1\\RHS$

Answer 2

$= \frac{ \tan^{2} }{1 + \tan^{2} } + \frac{ \cot^{2} }{1 + \cot^{2} } = 1 \\ = \frac{ \tan^{2} }{1 + \tan^{2} } + \frac{ \frac{1}{ \tan ^{2} } }{1 + \frac{1}{ \tan^{2} } } \\ = \frac{ \tan^{2} }{1 + \tan^{2} }$

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