यदि sin alpha = frac{{336}}{{625}} तथा 450^ci | vedclass

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Question

(c) $\sin \alpha  = \frac{{336}}{{625}}$

$\Rightarrow$ $\cos \alpha  =  - \sqrt {1 - {{\sin }^2}\alpha }  =  - \sqrt

Vedclass · Accepted Answer

$\frac{4}{5}$

Vedclass · Answer

(c) $\sin \alpha  = \frac{{336}}{{625}}$

$\Rightarrow$ $\cos \alpha  =  - \sqrt {1 - {{\sin }^2}\alpha }  =  - \sqrt {1 - {{\left( {\frac{{336}}{{625}}} ight)}^2}} $

                                               [ $\because \alpha $, $II$  चतुर्थांश में है]

अब $\cos \left( {\frac{\alpha }{2}} ight) =  - \sqrt {\frac{{1 + \cos \alpha }}{2}}  =  - \frac{7}{{25}}$     

                                                [ $\because \frac{\alpha }{2}$  $III$ चतुर्थांश में है]

$	herefore \,\,\,\sin \left( {\frac{\alpha }{4}} ight) =  + \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]

यदि $\sin \alpha = \frac{{336}}{{625}}$ तथा $450^\circ < \alpha < 540^\circ ,$ हो तो $\sin \left( {\frac{\alpha }{4}} \right) $ बराबर है

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