# Calculate the trigonometric sum

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

### Calculate the trigonometric sum

$$cos^2\frac{\pi}{8} + cos^2\frac{3\pi}{8} + cos^2\frac{5\pi}{8} + cos^2\frac{7\pi}{8} = ?$$
Guest

### Re: Calculate the trigonometric sum

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

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

$$\sin^2 x + \cos^2 x = 1$$
so
$$2\cos^2(\pi/8)+2\sin^2(\pi/8) = 2$$

Hope this helped,

R. Baber.
Guest

### Re: Calculate the trigonometric sum

Thank you very much.
Guest

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