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Question

Mathematics Question on Inverse Trigonometric Functions

If tan⁡−1x\tan^{-1} x + tan⁡−1y\tan^{-1} y = 2π3\frac{2\pi}{3 } , then cot⁡−1x\cot^{-1} x + cot⁡−1y\cot^{-1} y is equal to

A

π2\frac{\pi }{2 }

B

12\frac{ 1}{2 }

C

π3\frac{\pi }{ 3}

D

32\frac{\sqrt{ 3}}{2 }

Answer

π3\frac{\pi }{ 3}

Explanation

Solution

We have, tan⁡−1x+tan⁡−1y=2π3\tan ^{-1} x+\tan ^{-1} y=\frac{2 \pi}{3}
⇒π2−cot⁡−1x+π2−cot⁡−1y=2π3\Rightarrow \frac{\pi}{2}-\cot ^{-1} x+\frac{\pi}{2}-\cot ^{-1} y=\frac{2 \pi}{3}
⇒cot⁡−1x+cot⁡−1y=π−2π3=π3\Rightarrow \cot ^{-1} x+\cot ^{-1} y=\pi-\frac{2 \pi}{3}=\frac{\pi}{3}