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Question: The value of \(\cos ^ { - 1 } \left( \cos \frac { 5 \pi } { 3 } \right) + \sin ^ { - 1 } \left( \cos...

The value of cos⁡−1(cos⁡5π3)+sin⁡−1(cos⁡5π3)\cos ^ { - 1 } \left( \cos \frac { 5 \pi } { 3 } \right) + \sin ^ { - 1 } \left( \cos \frac { 5 \pi } { 3 } \right)is.

A

π2\frac { \pi } { 2 }

B

5π3\frac { 5 \pi } { 3 }

C

10π3\frac { 10 \pi } { 3 }

D

00

Answer

π2\frac { \pi } { 2 }

Explanation

Solution

cos⁡−1[cos⁡5π3]+sin⁡−1[cos⁡5π3]=π2\cos ^ { - 1 } \left[ \cos \frac { 5 \pi } { 3 } \right] + \sin ^ { - 1 } \left[ \frac { \cos 5 \pi } { 3 } \right] = \frac { \pi } { 2 }

( sin⁡−1x+cos⁡−1x=π2\sin ^ { - 1 } x + \cos ^ { - 1 } x = \frac { \pi } { 2 } ).