Question

please give me correct solution​

Answer 1

Answer:

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