Question

tan alpha - cot alpha / tan alpha + cot alpha = tan^2 alpha -1 / sec^2 alpha​

Answer 1

Step-by-step explanation:

$\frac{ \tan( \alpha ) - \cot( \alpha ) ) }{ \tan( \alpha ) + \cot( \alpha ) }$

take cotα

$\frac{ \frac{ \tan( \alpha ) }{ \cot( \alpha ) } - 1}{ \frac{{ \tan( \alpha ) } }{ \cot( \alpha ) } + 1 }$

$\frac{ { \tan( \alpha ) }^{2} - 1 }{ { \tan( \alpha ) }^{2} + 1 }$

1+tan^α= sec^2α

(tana/cota)= Tana *(1/cota)

= Tana *tana

= tan^2a