Question

If tanA=a/(a+1) and tanB=1/(2a+1) then find the value of A+B.

Answer 1

we know tan(A+B) =

( tanA+tanB)/(1-TanAtanB)

now putting values for tanA and tanB

[a/(a+1) +1/(2a+1)]/{1-a/(2a+1)(a+1)}

= (2a^2 +a +a+1)/(2a+1)(a+1) -a

= 2a^2+2a+1/2a^2+a+2a+1-a

=(2a^2 +2a +1) /( 2a^2 +2a+1)

= 1

hence Tan(A+B)= 1

Tan(A+B)= Tan45

A+B =45°