cos^2(x) + cos^2(pi - x)= 1
cos^2(x) + [ cos (pi)cos (x) + sin(pi) sin(x) ] ^2
cos^2(x) + [ - cos(x) ] ^2
cos^2(x) + cos^2(x)
2cos^2(x)
This is not an identity !!!
If the question was
\(\cos^2x+\cos^2(\frac{\pi}{2}-x)=1\)
Then it's a whole nother story!
\(cos^2(x) + cos^2(\pi - x)= 1\)
\(x=\mathbb{R}\) all together!
!
+128460 
!
