Question

Is LHS=RHS?

$\sqrt{\frac{cosec\theta -1}{cosec\theta +1}}+\sqrt{\frac{cosec\theta +1}{cosec\theta -1}}=2\cos \theta$

Say true or false?

• A. True
• B. False
• C. Ambiguous
• D. Data insufficient

Answer 1

The correct option is B False

Simplifying the given expression, we get
$\frac{cosec\theta -1+cosec\theta +1}{\sqrt{cose{c}^2\theta -1}}$

$=\frac{2cosec\theta }{cot\theta }$

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

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

$=2sec\theta$