Question

Solution of the equation $\frac{\tan 3x-\tan 2x}{1+\tan 3x\cdot \tan 2x}=1$ is given by $(n\in Z):$

• A. $x=n\pi +\pi /4$
• B. Solution does not exist
• C. $n\pi \pm \pi /4$
• D. None of these

Answer 1

The correct option is A $x=n\pi +\pi /4$

Given

$\frac{\tan 3x-\tan 2x}{1+\tan 3x.\tan 2x}$

$⟹\tan (3x-2x)=\tan x$

$⟹\tan x=1$

$⟹x=n\pi +\pi /4$