Question

If tanA=1/2 and tanB=1/3 and A,B are acute angles,then A+B​

Answer 1

Answer:

$\huge{ \bold{\boxed{ \pink{\dfrac{\pi}{4}}}}}$

Step-by-step explanation:

$tan \alpha = \dfrac{1}{2} \: and \: \: tan \beta = \dfrac{1}{3} \\ tan( \alpha + \beta ) = \dfrac{(tan \alpha + tan \beta )}{(1 - tan \alpha \: \: tan \beta )} \\ \\ = \dfrac{ \dfrac{1}{2} + \dfrac{1}{3} }{1 - \dfrac{1}{2} \times \: \dfrac{1}{3} } \\ \\ = \dfrac{ \dfrac{3 + 2}{6} }{1 - \dfrac{1}{6} } \\ \\ = \dfrac{ \dfrac{5}{6} }{ \dfrac{6 - 1}{6} } \\ \\ = \dfrac{ \dfrac{5}{6} }{ \dfrac{5}{6} } \\ \\ = 1$

$tan( \alpha + \beta ) = 1 \\ \\ tan( \alpha + \beta ) = tan \dfrac{\pi}{4} \\ \\ \alpha + \beta = \dfrac{\pi}{4}$