Question

2sin^2x-9 sinx cosx+7 cos^2x=0

Answer 1

$2sin^2x-9sinxcosx+7cos^2x=0\, |:cos^2x\ne 0\\\\2tg^2x-9tgx+7=0\\\\(tgx)_1=1,\; x_1=\frac{\pi}{4}+\pi n,\; n\in Z\\\\(tgx)_2=\frac{7}{2},\; x_2=arctg\frac{7}{2}+\pi n,\; n\in Z$