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

1 Answer
Ratnaker Mehta
May 14, 2018

# 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!

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