A value of tan−1⁡sin⁡cos−1⁡23, is

A value of $\tan^{- 1} \{\sin (\cos^{- 1} \sqrt{\frac{2}{3}})\}$ , is

A
$π / 4$
B
$π / 2$
C
$π / 3$
D
$π / 6$

Solution:

$\tan^{- 1} \{\sin (\cos^{- 1} \sqrt{\frac{2}{3}})\}$

$= \tan^{- 1} \{\sin (\sin^{- 1} \sqrt{\frac{1}{3}})\} = \tan^{- 1} \frac{1}{\sqrt{3}} = \frac{π}{6}$

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