Question

The value of $\cot \left({\tan }^{-1}\pi +{\tan }^{-1}\frac{1}{\pi }\right)+{\tan }^{-1}\sqrt{3}-{\sec }^{-1}(-2)$ is equal to

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

Answer 1

Answer: (A)

$\cot \left({\tan }^{-1}\pi +{\tan }^{-1}\frac{1}{\pi }\right)+{\tan }^{-1}\sqrt{3}-{\sec }^{-1}(-2)$
$=\cot \left({\tan }^{-1}\pi +{\cot }^{-1}\pi \right)+\frac{\pi }{3}-\frac{2\pi }{3}=\cot \left(\frac{\pi }{2}\right)-\frac{\pi }{3}=0-\frac{\pi }{3}=\frac{-\pi }{3}$