Find the principal value of each of the following :cosec-1(-\(\sqrt{2}

1.	Find the principal value of each of the following :cosec-1(-\(\sqrt{2}\))
Answer» \(cosec^{-1}(-\sqrt{2})=-cosec^{-1}(\sqrt{2})\) [Formula: cosec ^-1(-x) = -cosec ^-1(x) ] \(=-\frac{\pi}{4}\) Since cosec is negative in the third quadrant, the angle we are looking for will be in the third quadrant. \(=\pi+\frac{\pi}{4}\) \(=\frac{5\pi}{4}\)

Find the principal value of each of the following :cosec-1(-\(\sqrt{2}\))

Answer»

\(cosec^{-1}(-\sqrt{2})=-cosec^{-1}(\sqrt{2})\)

[Formula: cosec ^-1(-x) = -cosec ^-1(x) ]

\(=-\frac{\pi}{4}\)

Since cosec is negative in the third quadrant, the angle we are looking for will be in the third quadrant.

\(=\pi+\frac{\pi}{4}\)

\(=\frac{5\pi}{4}\)