Question

The value of ${\sin }^2\frac{\pi }{4}+{\sin }^2\frac{3\pi }{4}+{\sin }^2\frac{5\pi }{4}+{\sin }^2\frac{7\pi }{4}$ is

• A. $0$
• B. $1$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $2$

Given
${\sin }^2\frac{\pi }{4}+{\sin }^2\frac{3\pi }{4}+{\sin }^2\frac{5\pi }{4}+{\sin }^2\frac{7\pi }{4}$
$={\sin }^2\frac{\pi }{4}+{\sin }^2(\pi -\frac{\pi }{4})+{\sin }^2(\pi +\frac{\pi }{4})+{\sin }^2(2\pi -\frac{\pi }{4})={\sin }^2\frac{\pi }{4}+{\sin }^2\frac{\pi }{4}+{(-\sin \frac{\pi }{4})}^2+{(-\sin \frac{\pi }{4})}^2=4{\sin }^2\frac{\pi }{4}=2$