5sinx=3cos^2x-5 ОДЗ IsinxI≤1
3cos^2x-5sin^2x-5cos^2x-5sinx=0
-2cos^2x-5sin^2x-5sinx=0
-2(1-sin^2x)-5sin^2x-5sinx=0
-3sin^2x-5sinx-2=0
3sin^2x+5sinx+2=0
sinx=t
3t^2+5t+2=0
D=b^2-4ac D=25-4*3*2=1 t12=(-5+-1)/6 t1=-1 t2=-2/3
sinx=-1 x=-π/2+2πn,n∈Z
sinx=-2/3
x=(-1)^(n=1)arcsin2/3+πn,n∈Z