Question

prove that tanA/(1+tan^2A)^2+cotA/(1+cotA^2)^2=sinAcosA​

Answer 1

ANSWER.... {¶}

$\frac{ \tan \alpha }{ {(1 + {tan}^{2} \alpha })^{2} } + \frac{ \cot \alpha }{ {(1 + {cot}^{2} \alpha })^{2} } \\ \\ \frac{ \tan \alpha }{ { \sec}^{4} \alpha } + \frac{ \cot \alpha }{ { cosec }^{ 4 } \alpha } \\ \\ \tan \alpha . {cos}^{4} \alpha + cot \alpha . {sin}^{4} \alpha \\ \\ sin \alpha . {cos}^{3} \alpha + cos \alpha . {sin}^{3} \alpha \\ \\ cos \alpha . \sin \alpha ( {cos}^{2} \alpha + {sin}^{2} \alpha ) \\ \\ cos \alpha .sin \alpha \\ \\ hence \: proved$