Question

If $\frac{1+\cos 2x}{\sin 2x}+3(1+(\tan x\left)\tan \frac{x}{2}\right)\sin x=4$, then the value of $\tan x$ can be equal to

• A. $1$
• B. $1/2$
• C. $3$
• D. $1/3$

Answer 1

Answer: (A), (D)

The correct options are
A $1$
D $1/3$

Mistake : ans is A,D

$\sin 2x=\frac{2\tan x}{1+{\tan }^{2}x},cos2x=\frac{1-{\tan }^{2}x}{1+{\tan }^{2}x}$

by using this on simplifying using $\tan \frac{x}{2}=t$;

$\frac{1-t^2}{2t}+3(1+\frac{2t}{1-t^2})\frac{2t}{1+t^2}=\frac{1-t^2}{2t}+3(\frac{1+t^2}{1-t^2})\frac{2t}{1+t^2}$

on simplifying;

$\cot x+3\tan x=4$

$\tan x=1,\frac{1}{3}$