Question

If $\cot x-\tan x=2,$ then generalized solution is (here $n$ is integer)

• A. $x=2n\pi +\frac{\pi }{2}$
• B. $x=n\pi +\frac{\pi }{4}$
• C. $x=\frac{n\pi }{2}+\frac{\pi }{8}$
• D. $x=\frac{n\pi }{2}+\frac{\pi }{16}$

Answer 1

The correct option is C $x=\frac{n\pi }{2}+\frac{\pi }{8}$

$\cot x-\tan x=2\Rightarrow 1-{\tan }^{2}x=2\tan x\Rightarrow 1=\frac{2\tan x}{1-{\tan }^{2}x}\Rightarrow \tan 2x=1\Rightarrow 2x=n\pi +\frac{\pi }{4}\Rightarrow x=\frac{n\pi }{2}+\frac{\pi }{8}$