Write the value of [ ( 2 )+ ^ -1 (1 3 ) ] - Vidyadip

Question

Write the value of $\cos \left[\left(\frac{\pi}{2}\right)+\sin ^{-1}\left(\frac{1}{3}\right)\right]$

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Answer

suppose $\sin ^{-1} \frac{1}{3}=\theta$
$
\begin{aligned}
\therefore \quad \cos \left(\frac{\pi}{2}+\theta\right)=-\sin \theta & =-\sin \left(\sin ^{-1}\left(\frac{1}{3}\right)\right) \\
& =-\left(\frac{1}{3}\right)=-\frac{1}{3} \text { }
\end{aligned}
$

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