Question

prove :
A + B = π/4 if tanA = m/m+1 , tanB = 1/2m+1
(m ≥ 0)
pls help....

Answer 1

tan(A+B) = tanA + tanB / 1 - tanAtanB

= m/m+1 + 1/2m+1 / 1 - (m/m+1* 1/2m+1)
=( m(2m+1) + m + 1)/ (m+1)(2m+1) * (2m+1)(m+1)/(2m+1)(m+1) - m

= 2m^2 + 2m +1 /2m^2 + 2m + 1
= 1

so tan(A+B) = 1
and A+B = 45degrees = pi/4 radians

Answer 2

thanks a lot.. :)