Question

The value of ${\displaystyle {\cos }^2 \frac{\pi }{16}+{\cos }^2 \frac{3\pi }{16}+{\cos }^2 \frac{5\pi }{16}+{\cos }^2 \frac{7\pi }{16}}$ is ______.

विकल्प

• 2

• 1

• 0

• None of these

Answer 1

The value of ${\displaystyle {\cos }^2 \frac{\pi }{16}+{\cos }^2 \frac{3\pi }{16}+{\cos }^2 \frac{5\pi }{16}+{\cos }^2 \frac{7\pi }{16}}$ is 2.

Explanation:

${\displaystyle {\cos }^2 \frac{\pi }{16}+{\cos }^2 \frac{3\pi }{16}+{\cos }^2 \frac{5\pi }{16}+{\cos }^2 \frac{7\pi }{16}}$

${\displaystyle {\cos }^2 \frac{\pi }{16}+{\cos }^2 \frac{3\pi }{16}+{\cos }^2(\frac{\pi }{2}-\frac{3\pi }{16})+{\cos }^2(\frac{\pi }{2}-\frac{\pi }{16})}$

= ${\displaystyle {\cos }^2 \frac{\pi }{16}+{\cos }^2 \frac{3\pi }{16}+{\sin }^2 \frac{3\pi }{16}+{\sin }^2 \frac{\pi }{16}}$

= 1 + 1

= 2