Discussion

Explanation:

Given, ${\cos }^2\frac{\mathrm{\pi }}{8}$ + ${\cos }^2\frac{3\mathrm{\pi }}{8}$ + ${\cos }^2\frac{5\mathrm{\pi }}{8}$ + ${\cos }^2\frac{7\mathrm{\pi }}{8}$

= ${\cos }^2\frac{\mathrm{\pi }}{8}$ + ${\cos }^2\frac{3\mathrm{\pi }}{8}$ + ${\cos }^2\left(\frac{\mathrm{\pi }}{2}+\frac{\mathrm{\pi }}{8}\right)$ + ${\cos }^2\left(\frac{\mathrm{\pi }}{2}+\frac{3\mathrm{\pi }}{8}\right)$

= ${\cos }^2\frac{\mathrm{\pi }}{8}$ + ${\cos }^2\frac{3\mathrm{\pi }}{8}$ + ${\sin }^2\frac{\mathrm{\pi }}{8}$ + ${\sin }^2\frac{3\mathrm{\pi }}{8}$

= ${\cos }^2\frac{\mathrm{\pi }}{8}$ + ${\sin }^2\frac{\mathrm{\pi }}{8}$ + ${\cos }^2\frac{3\mathrm{\pi }}{8}$ +  + ${\sin }^2\frac{3\mathrm{\pi }}{8}$

= 1 + 1 = 2

Hence, option (c).

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