Sin^2x+sinx*cosx-2cos^2x=0
sin^2x+sinxcosx -2 +2sin^2x=0
3sin^2x +sinxcosx -2 =0
3sin^2x +sinxcosx -2sin^2x - 2cos^2x =0
sin^2x +sinxcosx -2cos^2x =0 | /cos^2x
tg^2x +tgx -2 =0
делаем замену:
tgx = t
t^2 + t -2 = 0
d= 1- 4* 1 * (-2) = 9
x1 = -1+3/2 =1;
x2= -1-3/2 = -2;
tgx = 1 tgx=-2
tgx = 1:
x=arctg1 + pn, n e z ;
x= p/4 +pn, nez;
tgx = -2 :
x= arctg ( -2 ) + pk, k e z;
ответ : p/4 + pn, nez ; arctg (-2) +pk, k e z.
Фууух :)