Question

Solve : ${\sin }^2\frac{\pi }{7}.{\sin }^2\frac{5\pi }{14}.{\sin }^2\frac{8\pi }{7}.{\sin }^2\frac{9\pi }{14}$

Answer 1

${\sin }^2\frac{\pi }{7}$$.{\sin }^2(\frac{\pi }{2}-\frac{\pi }{7})$$.{\sin }^2\frac{8\pi }{7}$$.{\sin }^2(\frac{\pi }{2}-\frac{8\pi }{7})$

${\sin }^2\frac{\pi }{7}$$.{\cos }^2\frac{\pi }{7}$$.{\sin }^2\frac{8\pi }{7}$$.{\cos }^2\frac{8\pi }{7}$

$(\sin \frac{\pi }{7}$$.\cos \frac{\pi }{7}{)}^2$$.\left(\sin \right(\pi +\frac{\pi }{7})$$.\cos (\pi +\frac{\pi }{7}){)}^2$

$(\sin \frac{\pi }{7}$$.\cos \frac{\pi }{7}{)}^2$$.(-\sin \frac{\pi }{7}$$.(-\cos (\frac{\pi }{7}){)}^2$

$(\sin \frac{\pi }{7}$$.\cos \frac{\pi }{7}{)}^4$

$(\frac{\sin \frac{2\pi }{7}}{2}{)}^4$

$\frac{1}{16}(\sin \frac{\pi }{7}{)}^4$

now $\sin \frac{2\pi }{7}=0.7818$

$\frac{1}{16}(0.7818{)}^4=\frac{0.37}{16}$