sin^2 x - 3sin2x + 5cos^2 x = 0
First let us rewrite:
We know that:
sin2x = 2sinx*cosx
Now substitute:
sin^2 x - 3*2sinx*cosx + 5cos^2 x = 0
sin^2 x - 6sinx*cosx + 5cos^2 x= 0
Nw let us factor:
(sin-5cosx)(sinx - cosx) = 0
Then we have two cases:
sinx -5cosx = 0
==> sinx= 5cosx
==> tanx = 5
==> x= arctan 5 + 2kpi.
Also,
sinx-cosx = 0
==> sinx = cosx
==> x= pi/4 + 2kpi