- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
medium
${\sin ^2}\frac{\pi }{8} + {\sin ^2}\frac{{3\pi }}{8} + {\sin ^2}\frac{{5\pi }}{8} + {\sin ^2}\frac{{7\pi }}{8} = $
A
$1$
B
$-1$
C
$0$
D
$2$
Solution
(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$.
Standard 11
Mathematics
