class 12 maths inverse trigonometric functions

$\frac{{9\pi }}{8} - \frac{9}{4}{\sin ^{ - 1}}\frac{1}{3} = \frac{9}{4}{\sin ^{ - 1}}\frac{{2\sqrt 2 }}{3}$

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📘 Inverse Trigonometric Functions NCERT Misc. , Q.12 , Page 52 SA

$\frac{{9\pi }}{8} - \frac{9}{4}{\sin ^{ - 1}}\frac{1}{3} = \frac{9}{4}{\sin ^{ - 1}}\frac{{2\sqrt 2 }}{3}$

Official Solution

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$\frac{{9\pi }}{8} - \frac{9}{4}{\sin ^{ - 1}}\frac{1}{3}$

$= \frac{9}{4}\left[ {\frac{\pi }{2} - {{\sin }^{ - 1}}\frac{1}{3}} \right] = \frac{9}{4}{\cos ^{ - 1}}\frac{1}{3} = \frac{9}{4}{\sin ^{ - 1}}\left( {\frac{{2\sqrt 2 }}{3}} \right)$

Hence, L.H.S. = R.H.S.

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