Question

Prove the following identities:
[1/(sec theta - tan theta)] = (sec theta + tan theta)​

Answer 1

Hope it will be helpful ... Here Q is theta everywhere

Rationalising LHS

1/sec Q -tan Q × sec Q + tan Q / sec Q - tan Q

SecQ + tanQ / sec2 Q - tan2 Q

SecQ + tan Q / 1

SecQ + tan Q

Therefore LHS = RHS

Answer 2

$\mathfrak{\underline{solution}}$

We have,