^2 8 + ^2 3 8 + ^2 5 8 + ^2 7 8 = - Vidyadip

Question

${\sin ^2}\frac{\pi }{8} + {\sin ^2}\frac{{3\pi }}{8} + {\sin ^2}\frac{{5\pi }}{8} + {\sin ^2}\frac{{7\pi }}{8} = $

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Answer

d
(d) ${\sin ^2}\frac{\pi }{8} + {\sin ^2}\frac{{3\pi }}{8} + {\sin ^2}\frac{{5\pi }}{8} + {\sin ^2}\frac{{7\pi }}{8}$

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

$ = 2\left( {{{\sin }^2}\frac{\pi }{8} + {{\sin }^2}\frac{{3\pi }}{8}} \right) = 2 \times 1 = 2$.

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