Question

Which of the following is the principal value branch of cosec^–1x?

पर्याय

• ${\displaystyle (\frac{-\pi }{2},\frac{\pi }{2})}$

• ${\displaystyle [0,\pi ]-\left\{\frac{\pi }{2}\right\}}$

• ${\displaystyle [\frac{-\pi }{2},\frac{\pi }{2}]}$

• ${\displaystyle [\frac{-\pi }{2},\frac{\pi }{2}]-\left\{0\right\}}$

Answer 1

${\displaystyle [\frac{-\pi }{2},\frac{\pi }{2}]-\left\{0\right\}}$

Explanation:

Principal value branch of cosec^–1x is

${\displaystyle [\frac{-\pi }{2},\frac{\pi }{2}]-\left\{0\right\}}$ as cosec^–1(0) = ${\displaystyle \infty }$ (not defined).