Question

Cos^2x-3sinx*cosx= -1

Answer 1

$cos^2x-3sinxcosx= -1\\cos^2x-3sinxcosx=-sin^2x-cos^2x\\2cos^2x-3sinxcosx+sin^2x=0|:cos^2x,\;cosx \neq 0,\;x \neq \frac{\pi}{2}+\pi n,\;n\in Z\\tg^2x-3tgx+2=0, \quad tgx=u\\u^2-3u+2=0\\D:9-8=1\\u_1,_2=\frac{3\pm1}{2}, \quad u_1=2, \; \; u_2=1\\\\tgx_1=2\\x_1=arctg2+\pi n. \; n\in Z;\\\\tgx_2=1\\x_2=\frac{\pi}{4}+\pi n, \; n\in Z.$