Question

find the appropriate value from picture

Answer 1

$\alpha + \beta = 90 \\ \beta = 90 - \alpha \\ = \frac{ \tan( \alpha ) }{ \tan( 90 - \alpha ) } + \sin^{2} (90 - \alpha ) + \sin^{2} \alpha \\ = \frac{ \tan( \alpha ) }{ \cot( \alpha ) } + \cos^{2} \alpha + \sin^{2} \alpha \\ = \frac{ \tan( \alpha ) }{ \frac{1}{ \tan( \alpha ) } } +1 \\ = \ \tan ^{2} \alpha+1 =sec^{2}\alpha$
option D is correct.