The principal value of ^ - 1 [ ( 2 3 ) ] is - Vidyadip

MCQ

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

A
$ - \frac{{2\pi }}{3}$
B
$\frac{{2\pi }}{3}$
C
$\frac{{4\pi }}{3}$
✓
None of these

✓

Answer

Correct option: D.

None of these

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

$ = {\sin ^{ - 1}}\sin \left( {\frac{\pi }{3}} \right) = \frac{\pi }{3}$ .

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