Question

$1-3cos^{2}x = 2sinxcosx$

Answer 1

$1-3cos^2x=2\, sinx\, cosx\\\\sin^2x+cos^2x-3cos^2x=2sinx\, cosx\\\\sin^2x-2\, sinx\, cosx-2cos^2x=0\, |:cos^2x\ne 0\\\\tg^2x-2\, tgx-2=0\\\\D/4=1+2=3\; ,\; \; tgx=1\pm \sqrt3\\\\tgx=1-\sqrt3\; ,\; \; x=arctg(1-\sqrt3)+\pi n\; ,\; n\in Z\\\\tgx=1+\sqrt3\; ,\; \; x=arctg(1+\sqrt3)+\pi k\; ,\; k\in Z$