Question

State true or false.
$\frac{\cos \theta }{\cos ec\theta +1}+\frac{\cos \theta }{\cos ec\theta -1}=1.$

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{\cos \theta }{\csc \theta +1}+\frac{\cos \theta }{\csc \theta -1}$

$=\cos \theta [\frac{1}{\csc \theta +1}+\frac{1}{\csc \theta -1}]$

$=\cos \theta \left[\frac{\csc \theta -1+\csc \theta +1}{{\csc }^2\theta -1}\right]$

$=\cos \theta \left[\frac{2\csc \theta }{{\cot }^2\theta }\right]$

$=\cos \theta \times \frac{2}{\sin \theta }{\tan }^2\theta =2\cot \theta {\tan }^2\theta =2\tan \theta$

Hence the given statement is false.