Question

2sin²x-sinxcosx-cos²x=0

Answer 1

$2sin^{2}x-sinxcosx-cos^{2}x=0 |:cos^{2}x\\2tg^{2}x-tgx-1=0\\\\tgx=u\\2u^{2}-u-1=0\\D:1+8=9\\u_1,_2= \frac{1\pm 3}{4}\\u_1=1\\u_2 =-\frac{1}{2}\\\\tgx=1\\x= \frac{\pi}{4} +\pi n,n\in Z\\\\tgx= -\frac{1}{2}\\x=-arctg \frac{1}{2}+\pi n,n\in Z$