For the principal values, evaluate each of the following:\(sin^{-1}(-\

1.	For the principal values, evaluate each of the following:\(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\)
Answer» \(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\) \(=-\frac{\pi}3+\frac{\pi}6\) {Since sin^-1x = An angle in\([-\frac{\pi}2,\frac{\pi}2]\) whose sine is x, Similarly, cos^-1= An angle in [0, π ] whose cosine is x} \(=-\frac{\pi}6\) Hence, \(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\) = \(-\frac{\pi}6\) \(\therefore\) Principal value of \(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\) is \(-\frac{\pi}6\)

For the principal values, evaluate each of the following:\(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\)

Answer»

\(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\)

\(=-\frac{\pi}3+\frac{\pi}6\)

{Since sin^-1x = An angle in\([-\frac{\pi}2,\frac{\pi}2]\) whose sine is x, Similarly, cos^-1= An angle in [0, π ] whose cosine is x}

\(=-\frac{\pi}6\)

Hence,

\(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\) = \(-\frac{\pi}6\)

\(\therefore\) Principal value of \(sin^{-1}(-\frac{\sqrt3}2)+cos^{-1}(\frac{\sqrt3}2)\) is \(-\frac{\pi}6\)