How to prove cos^2(pi/8)+cos^2 ((3pi)/8)+cos^2((5pi)/8)+cos^2((7pi)/8)=2 ?

1 Answer
Jul 11, 2018

Please see below

Explanation:

Let pi/8=x then 8x=pi and 4x=pi/2

LHS=cos^2(pi/8)+cos^2((3pi)/8)+cos^2((5pi)/8)+cos^2((7pi)/8)

=cos^2x+cos^2(3x)+cos^2(5x)+cos^2(7x)

=cos^2x+cos^2(3x)+cos^2(4x+x)+cos^2(4x+3x)

=cos^2x+cos^2(3x)+cos^2(pi/2+x)+cos^2(pi/2+3x)

=cos^2x+cos^2(3x)+sin^2(x)+sin^2(3x)=1+1=2=RHS