Sin^2x-5 cosx=sinx*cosx-5sinx...

Sin^2x-5 cosx=sinx*cosx-5sinx

 

sin^2x-5 cosx=sinx*cosx-5sinx
sin^2x - 5cosx - sinxcosx + 5sinx = 0
sin^2x + 5sinx - 5cosx - sinxcosx = 0
sinx(sinx + 5) - cosx(5 + sinx) = 0
(sinx - cosx)(sinx + 5) = 0
sinx - cosx = 0 | : cosx
tgx - 1 = 0
tgx = 1
x = arctg1 + pin
x = pi/4 + pin, n = Z
sinx + 5 = 0
sinx = -5
x = (-1)^n * -arcsin5 + pin, n=Z