Question

Prove that

$\sqrt{\frac{sec\theta -1}{sec\theta +1}}+\sqrt{\frac{sec\theta +1}{sec\theta -1}}=2cosec\theta$ [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

$\sqrt{\frac{sec\theta -1}{sec\theta +1}}+\sqrt{\frac{sec\theta +1}{sec\theta -1}}$

$=\frac{(\sqrt{sec\theta -1}{)}^2+(\sqrt{sec\theta +1}{)}^2}{\sqrt{se{c}^2\theta -1^2}}$

$=\frac{sec\theta -1+sec\theta +1}{\sqrt{se{c}^2\theta -1}}$

$=\frac{2sec\theta }{\sqrt{ta{n}^2\theta }}$

$=\frac{2sec\theta }{tan\theta }$

$=\frac{2\frac{1}{cos\theta }}{\frac{sin\theta }{cos\theta }}$

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

$=2cosec\theta$