Question
If ${\tan ^{ - 1}}x + {\tan ^{ - 1}}y = \frac{{4\pi }}{5}$, then ${\cot ^{ - 1}}x + {\cot ^{ - 1}}y$ equals to
- (a) $\frac{\pi }{5}$ ✓ Correct
- (b) $\frac{{2\pi }}{5}$
- (c) $\frac{{3\pi }}{5}$
- (d) $\pi$
Inverse Trigonometric Functions — Class 12 Maths Solution
Step-by-step Solution
We have, ${\tan ^{ - 1}}x + {\tan ^{ - 1}}y = \frac{{4\pi }}{5}$
$\Rightarrow$ $\frac{\pi }{2} - {\cot ^{ - 1}}x + \frac{\pi }{2} - {\cot ^{ - 1}}y = \frac{{4\pi }}{5}$
$\Rightarrow$ $- \left( {{{\cot }^{ - 1}}x + {{\cot }^{ - 1}}y} \right) = \frac{{4\pi }}{5} - \pi$
$\Rightarrow$ ${\cot ^{ - 1}}x + {\cot ^{ - 1}}y = - \left( { - \frac{\pi }{5}} \right)$
$\Rightarrow$ ${\cot ^{ - 1}}x + {\cot ^{ - 1}}y = \frac{\pi }{5}$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Inverse Trigonometric Functions. Curated by Sachin Sharma. Free for all students.