A) \[\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}\]
B) \[\sqrt{\sqrt{2}-1}\]
C) \[\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}\]
D) None of these
Correct Answer: C
Solution :
We know, \[{{\sin }^{2}}A=\left( \frac{1-\cos 2A}{2} \right)\] \[\Rightarrow \] \[{{\sin }^{2}}(22{}^\circ 30)=\frac{1-\cos {{45}^{o}}}{2}\] \[=\frac{\left( 1-\frac{1}{\sqrt{2}} \right)}{2}\] \[=\frac{\sqrt{2}-1}{2\sqrt{2}}\] \[\Rightarrow \] \[\sin (22{}^\circ 30)=\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}\]
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