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Integration by Substitution

The value of ...

Question

The value of $t a n^{- 1} \frac{1}{2} + t a n^{- 1} \frac{1}{3}$ is

A

π/4

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B

π/6

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C

π/3

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D

0

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Solution

The correct option is A
π/4

$t a n^{- 1} \frac{1}{2} + t a n^{- 1} \frac{1}{3} = t a n 6 - 1 \frac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{2} . \frac{1}{3}} = t a n^{- 1} (\frac{5 / 6}{5 / 6})$
$t a n^{- 1} 1 = \frac{π}{4}$

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