Question

Solve :$\frac{\tan 3x-\tan 2x}{1+\tan 3x\tan 2x}=1$

Answer 1

Using the fact, $\tan (a-b)=\frac{\tan a-\tan b}{1+\tan a\tan b}$
The above equation can be written as :
$\tan x=1$
$⟹x=n\pi +\frac{\pi }{4}$
But whenever $x=n\pi +\frac{\pi }{4}$, then $2x=2n\pi +\pi /2$ and $\tan 2x$ will be be undefined.
As $\tan 2x$ was there in the original question, a correct solution cannot make it undefined.
Therefore, there is no solution to the above equation.