Question 888438
You're alright up to there although you could have just stayed with cosine.
{{{-sin^2(x)=0}}}
Multiply both sides by (-1).
{{{sin^2(x)=0}}}
Take the square root of both sides. 
{{{sin(x)=0}}}
Now, which values of {{{x}}} give you a value of {{{0}}}?
There are two of them. 
{{{x=0}}}
and 
{{{x=pi}}}
.
.
.
For the cosine,
{{{cos^2(x)-1=0}}}
{{{cos^2(x)=1}}}
{{{cos(x)=0 +- 1}}} 
Also, two solutions.
{{{x=0}}} and
{{{x=pi}}}