Question

Please help me:
Prove this expression do not depend on x
"Cos^2(pi/4+x) + cos^2(pi/4-x)"

Answer 1

\(\large \cos(A) = \sin(\frac \pi2-A)\)
\(\large \cos(\frac \pi4+x) = \sin(\frac \pi2-\frac \pi4-x) = \sin(\frac \pi4-x)\)
\(\large \cos^2(\frac \pi4+x) + \cos^2(\frac \pi4-x) =
\sin^2(\frac \pi4-x) + \cos^2(\frac \pi4-x) = 1\)

Answer 2

yup that's right!