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}