Problem: If a=21 and (a+1)(b+1)=2, then the radian measure of Arctan a+ Arctan b equals
Answer Choices:
A. 2π
B. 3π
C. 4π
D. 5π
E. 6π
Solution:
Let x=Arctana and y=Arctanb :
(a+1)(b+1)=2(tanx+1)(tany+1)=2tanx+tany=1−tanxtanytan(x+y)=1−tanxtanytanx+tany=1x+y=4π.