Question

(1+tan^2A)cot A.
--------------------------. =tanA
cosec^2A​

Answer 1

Step-by-step explanation:

$\frac{(1 + { \tan( \alpha ) ) }^{2} \cot( \alpha ) }{ { \csc( \alpha ) }^{2} } = \frac{ { \sec( \alpha ) }^{2} \cot( \alpha ) }{ { \csc( \alpha ) }^{2} } = \frac{ \cot( \alpha ) { \sin( \alpha ) }^{2} }{ { \cos( \alpha ) }^{2} } \\ \\ = \frac{ \cot( \alpha ) \times { \tan( \alpha ) }^{2} }{1} \\ \\ = \tan( \alpha )$