A) \[-\frac{1}{\sqrt{10}}\]
B) \[\frac{1}{\sqrt{10}}\]
C) \[-\frac{1}{10}\]
D) \[\frac{1}{10}\]
Correct Answer: B
Solution :
We have \[\sin \left( \frac{1}{2}{{\cos }^{-1}}\frac{4}{5} \right)\] Now put \[\frac{4}{5}=\cos 2\theta \] \[\therefore \] \[\sin \left( \frac{1}{2}\times 2\theta \right)\] \[\sin \theta =\sqrt{\frac{1-\cos 2\theta }{2}}\] \[=\sqrt{\frac{1-\frac{4}{5}}{2}}=\sqrt{\frac{1}{5\times 2}}=\frac{1}{\sqrt{10}}\]
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