A) \[{{\sin }^{-1}}\left( \tan r \right)\]
B) \[{{\sin }^{-1}}\left( \tan r \right)\]
C) \[ta{{n}^{-1}}\left( \sin i \right)\]
D) \[cot\left( \tan i \right)\]
Correct Answer: B
Solution :
Here \[i=r\] \[r=90-r\] So, \[\mu =\frac{\sin r}{\sin r}=\frac{\sin \,\,(90-r)}{\sin r}\] \[\mu =\frac{\cos r}{\sin r}=\frac{1}{\tan r}\] but \[\mu =\frac{1}{\sin C}\] where C is the critical angle So, \[\frac{1}{\sin C}=\frac{1}{\tan r}\] \[\Rightarrow \] \[\sin C=\tan r\] or \[C={{\sin }^{-1}}(\tan r)\]You need to login to perform this action.
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