Question

The value of ${\text{cot}}^{-1}3+{\text{cosec}}^{-1}\sqrt{5}$ is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is D $\frac{\pi }{4}$

${\text{cot}}^{-1}3+{\text{cosec}}^{-1}\sqrt{5}$
$={\tan }^{-1}\frac{1}{3}+{\tan }^{-1}\frac{1}{2}$
$={\tan }^{-1}\left(\frac{\frac{1}{3}+\frac{1}{2}}{1-\frac{1}{3}\times \frac{1}{2}}\right)$
$={\tan }^{-1}\left(1\right)$
$=\frac{\pi }{4}$