If tanα = $$\frac{5}{3}$$​ and tanβ = 4, then α + β is:

Correct option is A

Given:

​$$\tan\alpha = \frac{5}{3}, \quad \tan\beta = 4$$​​

Formula Used:

$$\tan(\alpha + \beta) = \frac{\tan\alpha + \tan\beta}{1 - \tan\alpha \cdot \tan\beta}$$​​

Solution:
$$\tan(\alpha + \beta) = \frac{\frac{5}{3} + 4}{1 - \left(\frac{5}{3} \cdot 4\right)} = \frac{\frac{5 + 12}{3}}{1 - \frac{20}{3}} = \frac{\frac{17}{3}}{\frac{-17}{3}} = -1$$​​

So,

​$$\tan(\alpha + \beta) = -1 =\tan 135^\circ$$​

​$$\alpha + \beta = 135^\circ$$​