Inverse Trigonometric Functions — Class 12 Maths Solution

exemplar objective MCQ NCERT,Ex.2.3,Q.21,Page.37
Question

Which of the following is the principal value branch of ${{\mathop{\rm cosec}\nolimits} ^{ - 1}}x$ ?

  • (a) $\left( {\frac{{ - \pi }}{2},\frac{\pi }{2}} \right)$
  • (b) $[0,\pi ] - \left\{ {\frac{\pi }{2}} \right\}$
  • (c) $\left[ {\frac{\pi }{2},\frac{\pi }{2}} \right]$
  • (d) $\left[ {\frac{{ - \pi }}{2},\frac{\pi }{2}} \right] - [0]$ ✓ Correct
Step-by-step Solution
Correct answer: option (d)

We know that, the principal value branch of ${{\mathop{\rm cosec}\nolimits} ^{ - 1}}x$ is $\left[ {\frac{{ - \pi }}{2},\frac{\pi }{2}} \right] - 0$.

$therefore,$ $y = {{\mathop{\rm cosec}\nolimits} ^{ - 1}}x$

← All Inverse Trigonometric Functions solutions Practice tests →

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Inverse Trigonometric Functions. Curated by Sachin Sharma. Free for all students.