The value of $\sin{\left( \sin^{- 1}{\frac{1}{3} + \sec^{- 1}3} ight) + \cos\left( an^{- 1}{\frac{1}{2} + an^{- 1}2} ight)}$ is

Question

The value of $\sin{\left( \sin^{- 1}{\frac{1}{3} + \sec^{- 1}3} ight) + \cos\left( 	an^{- 1}{\frac{1}{2} + 	an^{- 1}2} ight)}$ is

Dr. Abubacker · Accepted Answer

(a)
$\sin{\left\lbrack \sin^{- 1}{\left( \frac{1}{3} ight) + \sec^{- 1}{(3)}} ightbrack + \cos\left\lbrack 	an^{- 1}\left( \frac{1}{2} ight) + 	an^{- 1}{(2)} ightbrack}$
$= \sin\left\lbrack \sin^{- 1}{\left( \frac{1}{3} ight) + \cos^{- 1}\left( \frac{1}{3} ight)} ightbrack\$
+$\cos\left\lbrack 	an^{- 1}{\left( \frac{1}{2} ight) + \cot^{- 1}\left( \frac{1}{2} ight)} ightbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  = \sin{\frac{\pi}{2} + \cos\frac{\pi}{2}}$
$\left\lbrack \because\sin^{- 1}{x + \cos^{- 1}{x = \frac{\pi}{2}\ and	an^{- 1}{x + \cot^{- 1}{x = \frac{\pi}{2}}}}} ightbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  = 1$

Q. The value of $\sin{\left( \sin^{- 1}{\frac{1}{3} + \sec^{- 1}3} \right) + \cos\left( \tan^{- 1}{\frac{1}{2} + \tan^{- 1}2} \right)}$ is

Explanation

Reviewed by Dr. Abubacker

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