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Question: The principal value of \(\sin ^ { - 1 } \left[ \sin \left( \frac { 2 \pi } { 3 } \right) \right]\) ...

The principal value of sin⁡−1[sin⁡(2π3)]\sin ^ { - 1 } \left[ \sin \left( \frac { 2 \pi } { 3 } \right) \right] is

A

−2π3- \frac { 2 \pi } { 3 }

B

2π3\frac { 2 \pi } { 3 }

C

4π3\frac { 4 \pi } { 3 }

D

None of these

Answer

None of these

Explanation

Solution

The principal vlaue of sin⁡−1[sin⁡(π−2π3)]\sin ^ { - 1 } \left[ \sin \left( \pi - \frac { 2 \pi } { 3 } \right) \right]

= sin⁡−1sin⁡(π3)=π3\sin ^ { - 1 } \sin \left( \frac { \pi } { 3 } \right) = \frac { \pi } { 3 }