Find in radian measure of arctan(1/2)+arctan(1/3)?

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Find in radian measure of arctan(1/2)+arctan(1/3)?

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Answer 1 · 2018-05-14T17:04:01

$\frac{π}{4}$ $pi/4$ .

Explanation:

Recall that, $a r c tan x + a r c tan y = a r c tan (\frac{x + y}{1 - x y}), 0 < x y < 1$ $arc tanx+arc tany=arc tan((x+y)/(1-xy)), 0 lt xy lt 1$ .

Accordingly, since, $0 < \frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6} < 1,$ $0 lt 1/2*1/3=1/6 lt 1,$

$a r c tan (\frac{1}{2}) + a r c tan (\frac{1}{3}) = a r c tan (\frac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{2} \cdot \frac{1}{3}})$ $arc tan(1/2)+arc tan(1/3)=arc tan ((1/2+1/3)/(1-1/2*1/3))$ ,

$= a r c tan (\frac{\frac{5}{6}}{\frac{5}{6}})$ $=arc tan ((5/6)/(5/6))$ ,

$= a r c tan 1$ $=arc tan 1$ ,

$= \frac{π}{4}$ $=pi/4$ , is the desired value!

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Find in radian measure of arctan(1/2)+arctan(1/3)?

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