Calculate the trigonometric sum

[Guest]

[tex]cos^2\frac{\pi}{8} + cos^2\frac{3\pi}{8} + cos^2\frac{5\pi}{8} + cos^2\frac{7\pi}{8} = ?[/tex]

[Guest]

[tex]\cos x = -\cos (\pi-x)[/tex]
so
[tex]\cos^2(\pi/8)+\cos^2(3\pi/8)+\cos^2(5\pi/8)+\cos^2(7\pi/8) = 2\cos^2(\pi/8)+2\cos^2(3\pi/8)[/tex]

[tex]\cos x = \sin (\pi/2-x)[/tex]
so
[tex]2\cos^2(\pi/8)+2\cos^2(3\pi/8) = 2\cos^2(\pi/8)+2\sin^2(\pi/8)[/tex]

[tex]\sin^2 x + \cos^2 x = 1[/tex]
so
[tex]2\cos^2(\pi/8)+2\sin^2(\pi/8) = 2[/tex]

Hope this helped,

R. Baber.

[Guest]

Thank you very much.