Question

please solve this question​

Answer 1

Answer:

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

Step-by-step explanation:

LHS = RHS .