The value of tan ^{-1} 2 + tan ^{-1} 3 is | vedclass

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(A) We use the formula $	an ^{-1} x + 	an ^{-1} y = \pi + 	an ^{-1} \left( \frac{x+y}{1-xy} ight)$ when $xy > 1$. Here,$x = 2$ and $y = 3$,so $xy

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$\left(\frac{3 \pi}{4}\right)^c$

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(A) We use the formula $	an ^{-1} x + 	an ^{-1} y = \pi + 	an ^{-1} \left( \frac{x+y}{1-xy} ight)$ when $xy > 1$. Here,$x = 2$ and $y = 3$,so $xy = 6 > 1$. Therefore,$	an ^{-1} 2 + 	an ^{-1} 3 = \pi + 	an ^{-1} \left( \frac{2+3}{1-(2)(3)} ight)$. $= \pi + 	an ^{-1} \left( \frac{5}{1-6} ight) = \pi + 	an ^{-1} (-1)$. $= \pi - \frac{\pi}{4} = \frac{3 \pi}{4}$. Thus,the value is $\left( \frac{3 \pi}{4} ight)^c$.

The value of $\tan ^{-1} 2 + \tan ^{-1} 3$ is

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