How to prove that α+β=π/4 ? When α=arctan(1/2) and β=arctan(1/3) ?
1 Answer
Mar 26, 2018
Recall that
#tan(alpha + beta) = (tan alpha + tan beta)/(1 - tanalphatanbeta)#
We know that
#tan(alpha + beta) = (1/2 + 1/3)/(1 - 1/2(1/3))#
#tan(alpha + beta) = (5/6)/(5/6)#
#tan(alpha + beta) = 1#
#alpha+ beta= arctan(1)#
#alpha + beta = pi/4#
As required.
Hopefully this helps!
