A) \[{{\sin }^{-1}}\left( \frac{\mu }{2} \right)\]
B) \[{{\sin }^{-1}}\sqrt{\frac{\mu -1}{2}}\]
C) \[2{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]
Correct Answer: C
Solution :
Given \[{{\delta }_{m}}=A,\] as \[\mu =\frac{\sin \,\left( \frac{A+{{\delta }_{m}}}{2} \right)}{\sin \,\left( \frac{A}{2} \right)}\] \[\Rightarrow \]\[\mu =\frac{\sin \left( \frac{A+A}{2} \right)}{\sin \left( \frac{A}{2} \right)}=2\cos \frac{A}{2}\Rightarrow A=2{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]
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