Question

Solve :${\sin }^2\frac{\pi }{8}+{\sin }^2\frac{3\pi }{8}+{\sin }^2\frac{5\pi }{8}+si{n}^2\frac{7\pi }{8}=2$

Answer 1

From question,

$si{n}^2\frac{\pi }{8}+si{n}^2(\frac{\pi }{2}-\frac{\pi }{8})+si{n}^2\frac{5\pi }{8}+si{n}^2(\frac{3\pi }{2}-\frac{5\pi }{8})$

$=si{n}^2\frac{\pi }{8}+co{s}^2\frac{\pi }{8}+si{n}^2\frac{5\pi }{8}+co{s}^2\frac{5\pi }{8}$ ......as.. ($si{n}^2\theta +co{s}^2\theta =1$)

$=1+1$

$=2$