A) \[\frac{-1}{\sqrt{10}}\]
B) \[\frac{1}{\sqrt{10}}\]
C) \[\frac{3}{\sqrt{10}}\]
D) \[\frac{-3}{\sqrt{10}}\]
Correct Answer: A
Solution :
\[\cos (\alpha /2)=-\sqrt{\frac{1+\cos \alpha }{2}}\] \[\cos \alpha =-\sqrt{1-{{\sin }^{2}}\alpha }\][\[\because \alpha \]lies in IIIrd Quadrant] \[=-\sqrt{1-\frac{9}{25}}=-\frac{4}{5}\] \[\therefore \,\,\,\cos (\alpha /2)=-\sqrt{\frac{1-\frac{4}{5}}{2}}=-\frac{1}{\sqrt{10}}\].
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