Question

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

Answer 1

`pi/4`.

Explanation:

Recall that, `arc tanx+arc tany=arc tan((x+y)/(1-xy)), 0 lt xy lt 1`.

Accordingly, since, `0 lt 1/2*1/3=1/6 lt 1,`

`arc tan(1/2)+arc tan(1/3)=arc tan ((1/2+1/3)/(1-1/2*1/3))`,

`=arc tan ((5/6)/(5/6))`,

`=arc tan 1`,

`=pi/4`, is the desired value!