Question

*16. If A and B are acute angles such that tan A = 3, tan B =
tan (A+B) = 1 -tan A tan B'
tan A +tan B
show that A + B = 45°
​

Answer 1

Step-by-step explanation:

Formula

$\tan ( A + B ) = \frac { \tan A + \tan B } { 1 - \tan A \tan B }$

Given is its inverse i.e. in your question it is given that

$\left. { \tan ( A + B ) = \frac { 1 - \tan A \tan B } { \tan A + \tan B } } \right.$

so basically tan (a+ b) = P =1/P

so P^2 = 1

hence either A + B is 45 degree or 225°

but it is given that A and B are acute so their sum can 't be greater than 180.

hence A + B is 45 degree