Find the principal value of the following :\(\sin\begin{Bmatrix}\frac{

1.	Find the principal value of the following :\(\sin\begin{Bmatrix}\frac{\pi}{3}-\sin^{-1}\left(\frac{-1}{2}\right)\end{Bmatrix}\)
Answer» \(\sin\begin{Bmatrix}\frac{\pi}{3}-\sin^{-1}\left(\frac{-1}{2}\right)\end{Bmatrix}\) [Formula: sin^-1(-x) = -sin ^-1x ] \(=\sin\begin{Bmatrix}\frac{\pi}{3}-\left(-\sin^{-1}\frac{1}{2}\right)\end{Bmatrix}\) \(=\sin\begin{Bmatrix}\frac{\pi}{3}+\sin^{-1}\left(\frac{1}{2}\right)\end{Bmatrix}\) Putting value of sin ^-1\(\left(\frac{1}{2}\right)\) \(=\sin\begin{Bmatrix}\frac{\pi}{3}+\frac{\pi}{6}\end{Bmatrix}\) \(=\sin\frac{3\pi}{6}=\sin\frac{\pi}{2}=1\)

Find the principal value of the following :\(\sin\begin{Bmatrix}\frac{\pi}{3}-\sin^{-1}\left(\frac{-1}{2}\right)\end{Bmatrix}\)

Answer»

\(\sin\begin{Bmatrix}\frac{\pi}{3}-\sin^{-1}\left(\frac{-1}{2}\right)\end{Bmatrix}\) [Formula: sin^-1(-x) = -sin ^-1x ]

\(=\sin\begin{Bmatrix}\frac{\pi}{3}-\left(-\sin^{-1}\frac{1}{2}\right)\end{Bmatrix}\)

\(=\sin\begin{Bmatrix}\frac{\pi}{3}+\sin^{-1}\left(\frac{1}{2}\right)\end{Bmatrix}\)

Putting value of sin ^-1\(\left(\frac{1}{2}\right)\)

\(=\sin\begin{Bmatrix}\frac{\pi}{3}+\frac{\pi}{6}\end{Bmatrix}\)

\(=\sin\frac{3\pi}{6}=\sin\frac{\pi}{2}=1\)