sin^2(-x)+cos^2(-x)

sin^2(-x)+cos^2(-x)

$$\boxed{
\begin{array}{ccc}
\sin(-x) &=& -\sin{x}\\
\cos(-x) &=& \cos(x)
\end{array}
}\\\\\\
\sin^2(-x)+\cos^2(-x)\\
=[-\sin(x)]^2+[cos(x)]^2\\
=\sin^2(x)+\cos^2(x)\\
=1$$

sin^2(-x)+cos^2(-x)

Let -x  = θ

So

sin^2 (θ) + cos^2 (θ)  = 1   {this is just a basic identity}