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यदि $\sin \alpha = \frac{{336}}{{625}}$ तथा $450^\circ < \alpha < 540^\circ ,$ हो तो $\sin \left( {\frac{\alpha }{4}} \right) $ बराबर है
$\frac{1}{{5\sqrt 2 }}$
$\frac{7}{25}$
$\frac{4}{5}$
$\frac{3}{5}$
Solution
(c) $\sin \alpha = \frac{{336}}{{625}}$
$\Rightarrow$ $\cos \alpha = – \sqrt {1 – {{\sin }^2}\alpha } = – \sqrt {1 – {{\left( {\frac{{336}}{{625}}} \right)}^2}} $
[ $\because \alpha $, $II$ चतुर्थांश में है]
अब $\cos \left( {\frac{\alpha }{2}} \right) = – \sqrt {\frac{{1 + \cos \alpha }}{2}} = – \frac{7}{{25}}$
[ $\because \frac{\alpha }{2}$ $III$ चतुर्थांश में है]
$\therefore \,\,\,\sin \left( {\frac{\alpha }{4}} \right) = + \sqrt {\frac{{1 – \cos (\alpha /2)}}{2}} = \sqrt {\frac{{1 + \frac{7}{{25}}}}{2}} = \frac{4}{5}$
[ $\because \frac{\alpha }{4}$ दूसरे चतुर्थांश में है]
