Inverse Trigonometric Functions — Class 12 Maths Solution

exemplar objective MCQ NCERT,Ex.2.3,Q.28,Page.38
Question

The value of ${\cos ^{ - 1}}\left( {\cos \frac{{3\pi }}{2}} \right)$ is

  • (a) $\frac{\pi }{2}$ ✓ Correct
  • (b) $\frac{{3\pi }}{2}$
  • (c) $\frac{{5\pi }}{2}$
  • (d) $\frac{{7\pi }}{2}$
Step-by-step Solution
Correct answer: option (a)

We have, ${\cos ^{ - 1}}\left( {\cos \frac{{3\pi }}{2}} \right)$

$= {\cos ^{ - 1}}\cos \left( {2\pi - \frac{\pi }{2}} \right)$

$= {\cos ^{ - 1}}\cos \left( {\frac{\pi }{2}} \right) = \frac{\pi }{2}$

Note
Remember that, ${\cos ^{ - 1}}\left( {\cos \frac{{3\pi }}{2}} \right) \ne \frac{{3\pi }}{2}$
$\frac{{3\pi }}{2} \notin (0,\pi )$

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