Question
The value of $2{\sec ^{ - 1}}2 + {\sin ^{ - 1}}\left( {\frac{1}{2}} \right)$ is
- (a) $\frac{\pi }{6}$
- (b) $\frac{{5\pi }}{6}$ ✓ Correct
- (c) $\frac{{7\pi }}{6}$
- (d) 1
Inverse Trigonometric Functions — Class 12 Maths Solution
Step-by-step Solution
We have, $2{\sec ^{ - 1}}2 + {\sin ^{ - 1}}\frac{1}{2} = 2{\sec ^{ - 1}}\sec \frac{\pi }{3} + {\sin ^{ - 1}}\sin \frac{\pi }{6}$
$= 2 \cdot \frac{\pi }{3} + \frac{\pi }{6}$ [and $\left. {{{\sin }^{ - 1}}(\sin x) = x} \right]$
$= \frac{{4\pi + \pi }}{6} = \frac{{5\pi }}{6}$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Inverse Trigonometric Functions. Curated by Sachin Sharma. Free for all students.