The value of $\cos^2\left(\frac{\pi}{8}\right) + \cos^2\left(\frac{3\pi}{8}\right) + \cos^2\left(\frac{5\pi}{8}\right) + \cos^2\left(\frac{7\pi}{8}\right)$ is

Question and options

The value of

\cos^2\left(\frac{\pi}{8}\right) + \cos^2\left(\frac{3\pi}{8}\right) + \cos^2\left(\frac{5\pi}{8}\right) + \cos^2\left(\frac{7\pi}{8}\right)

Correct answer: C - $2$

cos(3pi/8)=sin(pi/8), so cos^2(pi/8)+cos^2(3pi/8)=1; cos^2(5pi/8)=cos^2(3pi/8) and cos^2(7pi/8)=cos^2(pi/8), giving another 1. Total 2.