Question

1/sec-tan=sec+tan prove it

Answer 1

Hiii friend,


1/Sec theta - Tan theta = Sec theta + Tan theta


We have,


LHS = 1/Sec theta - Tan theta


=> 1/Sec theta - Tan theta × (Sec theta+Tan theta)/(Sec theta+Tan theta)


=> (Sec theta+Tan theta)/(Sec²thta-Tan²theta)


=> Sec theta + Tan theta = RHS


Hence,


LHS = RHS.....PROVED.....

HOPE IT WILL HELP YOU..... :-)

Answer 2

solution:-

given by:-

$\frac{1}{ \sec( \theta) - \tan(\theta) } \\ \frac{1}{ \sec( \theta) - \tan(\theta) } \times \frac{ \sec( \theta) + \tan( \theta) }{ \sec( \theta) + \tan( \theta) } \\ \frac{ \sec( \theta) + \tan( \theta) }{ { \sec }^{2} \theta - { \tan }^{2} \theta} \\ \sec( \theta) + \tan( \theta) = \sec( \theta) + \tan( \theta) \\ (lhs = rhs )proved$