Question

Prove that :
$\frac{ \sin( \alpha ) \times \sec( \alpha ) }{ \csc( \alpha ) \times \cos( \alpha ) } = { \tan(\alpha ) }^{2}$
​

Answer 1

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

Here is your answer

☺HOPE IT IS HELPFUL ☺