Question

Prove the identities, where angles involved are acute angle for which the expression are defined.

Answer 1

$\sqrt{ \dfrac{1 + \sin a}{1 - \sin a} } \\ \\ \\ \sqrt{ \dfrac{1 + \sin a}{1 - \sin a} \times \frac{ 1 + \sin \: a }{1 + \sin a {}^{2} } } \\ \\ \\ \sqrt{ \dfrac{(1 + \sin a ) {}^{2} }{1 - { \sin }^{2}a } } \\ \\ \\ \sqrt{ \dfrac{ (1 + \sin a) {}^{2} }{ { \cos}^{2} a} } \\ \\ \\ \frac{1 + \sin a}{ \cos a} \\ \\ \\ \frac{ 1}{ \cos a} + \frac{ \sin a}{ \cos a}$


sec a + tan a



Proved.