Question

Is LHS=RHS?
$\sqrt{\frac{cosec\theta -\cot \theta }{cosec\theta +\cot \theta }}=\frac{1}{cosec\theta +\cot \theta }$

• A. Yes
• B. No
• C. Can't say
• D. Data insufficient

Answer 1

Answer: (A)

Yes

$L.H.S$ $=\sqrt{\frac{cosec\theta -\cot \theta }{cosec\theta +\cot \theta }\times \frac{cosec\theta +cot\theta }{cosec\theta +cot\theta }}$
$=\sqrt{\frac{(cose{c}^2\theta -co{t}^2\theta )}{(cosec\theta +cot\theta {)}^2}}$
$=\frac{1}{\sqrt{(cosec\theta +cot\theta {)}^2}}$
$=\frac{1}{(cosec\theta +cot\theta )}=R.H.S$