Question

решить уравнение:
3cos^2x+2sinxcosx-sin^2x=0

Answer 1

$3cos^2x+2sinxcosx-sin^2x=0|:(-cos^2x), \cosx neq 0,;x neq frac{pi}{2}+pi n,; n in Z;\tg^2x-2tgx-3=0, quad tgx=u\u^2-2u-3=0\frac{D}{4}:; (frac{2}{2})^2+3=4\t_1, _2=1pm 2, quad u_1=3, quad u_2=-1;\\tgx_1=3\x_1=arctg3+pi n, ; nin Z;\\tgx_2=-1\x_2=-frac{pi}{4}+pi n, ; nin Z.$