Question

Prove that

$\sqrt{\frac{1+sin\theta }{1-sin\theta }}+\sqrt{\frac{1-sin\theta }{1+sin\theta }}=2sec\theta$ [2 MARKS]

Answer 1

Concept: 1 Mark
Applicaiton: 2 Mark

We have

$=\frac{\sqrt{1+sin\theta }}{\sqrt{1-sin\theta }}+\frac{\sqrt{1-sin\theta }}{\sqrt{1+sin\theta }}$

$=\frac{1+sin\theta +1-sin\theta }{\sqrt{(1-sin\theta )(1+sin\theta )}}$

$=\frac{2}{\sqrt{(1-si{n}^2\theta )}}$

$=\frac{2}{\sqrt{co{s}^2\theta }}$

$=\frac{2}{cos\theta }$

$=2sec\theta$

$\therefore$ LHS = RHS