# For all real values of x,

Question:

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

(a) $\tan 2 x$

(b) $\tan x$

(c) $-\cot 3 x$

(d) none of these

Solution:

(b) $\tan x$

We have,

$\cot x-2 \cot 2 x=\cot x-2 \frac{\cot ^{2} x-1}{2 \cot x}$

$=\frac{\cot ^{2} x-\cot ^{2} x+1}{\cot x}$

$=\frac{1}{\cot x}$

$=\tan x$