Question

Solve the following equation:
$3{\sin }^{2}x-2\sin x\cos x-{\cos }^{2}x=0$

Answer 1

${3\sin }^{2}x-2\sin x\cos x-{\cos }^{2}x=0$

${3\sin }^{2}x-3\sin x\cos x+\sin x\cos x-{\cos }^{2}x=0$

$(\sin x-\cos x)(3\sin x+\cos x)=0$

Either, $\sin x-\cos x=0$

$\tan x=1,x=n\pi +\frac{\pi }{4}$

or, $3\sin x+\cos x=0$

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

$x=n\pi -{\tan }^{-1}\left(\frac{1}{3}\right)$