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Question

Question: \[\tan^{- 1}\frac{1}{2} + \tan^{- 1}\frac{1}{3} =\]...

tan⁡−112+tan⁡−113=\tan^{- 1}\frac{1}{2} + \tan^{- 1}\frac{1}{3} =

A

0

B

π/4\pi/4

C

π/2\pi/2

D

π\pi

Answer

π/4\pi/4

Explanation

Solution

tan⁡−112+tan⁡−113=tan⁡−112+131−12.13=tan⁡−11=π4\tan^{- 1}\frac{1}{2} + \tan^{- 1}\frac{1}{3} = \tan^{- 1}\frac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{2}.\frac{1}{3}} = \tan^{- 1}1 = \frac{\pi}{4}