Question

For all real values of $\theta$ , $\cot \theta -2\cot 2\theta$ is equal to

• A. $\tan 2\theta$
• B. $\tan \theta$
• C. $-\cot 3\theta$
• D. $\cot \theta$

Answer 1

Answer: (B)

$\tan \theta$

$\cot \theta -2\cot 2\theta$
$=\frac{\cos \theta }{\sin \theta }-\frac{2\cos 2\theta }{\sin 2\theta }$
$=\frac{\sin 2\theta .\cos \theta -2\cos 2\theta .\sin \theta }{\sin \theta \sin 2\theta }$

$=\frac{\sin (2\theta -\theta )-\cos 2\theta \sin \theta }{\sin \theta .\sin 2\theta }$
$=\frac{\sin \theta \{1-1+2{\sin }^2\theta \}}{\sin \theta .2\sin \theta \cos \theta }$
$=\tan \theta$
Hence, Option B is the correct option