Question

Given that tanAtanB = 3/4 , A + B = 45°, calculate the value of tan A + tan B.

Answer 1

the sum formula for the tangent, says that \[\tan(a+b) = \frac{\tan(a)+\tan(b)}{1-\tan (a)\tan(b)}\]

Answer 2

you are given that
\(\tan(A)\tan(B)=3/4\)

and \(A+B=45°\), so that
\[\tan(A+B)=\tan(45°)=1\]
Putting all this together
\[1=\frac{\tan(A)+\tan(B)}{1−3/4}\]
solve for this for \(\tan(A)+\tan(B)\)