5 sin ^2 x-2sin x cos x + cos ^3 x =4

Question

5 sin ^2 x-2sin x cos x + cos ^3 x =4

Answer 1

5sin^2-2sinxcosx+cos^3=4
5sin^2-2sinxcosx+cos^3-4sin^2-4cos^2=
sin^2-2sinxcosx-3cos^2=0/cos^2x
tg^2x-2tgx-3=0
D=4+12=16
tgx=3    x=arctg3+пк
tgx=-1    х=-п/4+пк