The value of cosec^-1 (2/√3) is: (a) π/4 (b) π/2 (c) π/3 (d) π/6

Question

The value of cosec^-1 (\(\frac{2}{\sqrt{3}}\)) is: 

(a) \(\frac{\pi}{4}\)

(b) \(\frac{\pi}{2}\)

(c) \(\frac{\pi}{3}\)

(d) \(\frac{\pi}{6}\)

Answer 1

(c) \(\frac{\pi}{3}\)

Let cosec^-1 (\(\frac{2}{\sqrt{3}}\)) 

\(\frac{2}{\sqrt{3}}\) = cosec A 

cosec A = \(\frac{2}{\sqrt{3}}\)

sin A = \(\frac{\sqrt{3}}{2}\) = sin 60° 

∴ A = 60° = \(\frac{\pi}{3}\)