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  4. The value of cot ( tan -1 π+ tan -1 (1/π))+ tan -1 √3- sec -1(-2) is equal to

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

Inverse Trigonometric Functions

Solution:

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