Question

Prove that $\sqrt{\frac{1+sinA}{1-sinA}}=secA+tanA$

Answer 1

LHS$=\sqrt{\frac{1+sinA}{1-sinA}}$

Multiply and divide LHS by $\sqrt{1+\sin A}$

$=\sqrt{\frac{1+\sin A}{1-\sin A}\times \frac{1+\sin A}{1+\sin A}}$

$=\frac{1+\sin A}{\cos A}$

$=\sec A+\tan A$

$=RHS$

Hence proved