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 **