A) \[{{\sin }^{-1}}(\sin \,r)\]
B) \[{{\sin }^{-1}}\,(\tan r')\]
C) \[{{\sin }^{-1}}\,(\tan i)\]
D) \[{{\tan }^{-1}}(\sin i)\]
Correct Answer: C
Solution :
\[_{D}{{\mu }_{R}}=\frac{\sin i}{\sin {r}'}{{\Rightarrow }_{R}}{{\mu }_{D}}=\frac{\sin {r}'}{\sin \ i}=\frac{1}{\sin C}\] \[\Rightarrow \sin C=\frac{\sin i}{\sin (90-r)}=\frac{\sin i}{\cos r}=\frac{\sin i}{\cos i}\] (as Ði = Ðr) \[\Rightarrow \sin C=\tan i\Rightarrow C={{\sin }^{-1}}(\tan i)\]
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