Question

if A and B are acute angles such that

$tan \: a \: = \: \frac{1}{3} \\ \\ tan \: b \: = \: \frac{1}{2}$


and Tan(A + B) =
$\frac{tan \: a \: + \: tan \: b}{1 \: - \: tan \: a \: tan \: b}$

Show that ,A + B = 45

Answer 1

The required answer.....!!!!!!!!!!

Answer 2

Here is your answer buddy,

$\textbf{GIVEN}$

Tan A = $\frac{1}{3}$
Tan B = $\frac{1}{2}$

Now we know that,

Tan(A+B) = $\frac{TanA+TanB}{1-TanATanB}$

=> Tan(A+B) = $\frac{1}{3} + \frac{1}{2}$ $\frac{1- \frac{1}{3}\frac{1}{2}$

=> Tan(A+B) = $\frac{2+3}{6} \frac{1-\frac{1}{6}$

=> Tan(A+B) = $\frac{5}{6}× \frac{6}{5}$

=> Tan(A+B) = 1

=> Tan(A+B) = Tan(45)

=> A+B = 45 degree.

Hope this helps you.
Be Brainly.