Given that \(\tan x = \frac{5}{12}\), and \(\tan y = \frac{3}{4}\), Find \(\tan (x + y)\).

A.

\(\frac{16}{33}\)

B.

\(\frac{33}{56}\)

C.

\(\frac{33}{16}\)

D.

\(\frac{56}{33}\)

Correct answer is D

\(\tan (x + y) = \frac{\tan x + \tan y}{1 - \tan x\tan y}\)

\(\tan x = \frac{5}{12} ; \tan y = \frac{3}{4}\)

\(\tan (x + y) = \frac{\frac{5}{12} + \frac{3}{4}}{1 - (\frac{5}{12} \times \frac{3}{4}})\)

= \(\frac{\frac{14}{12}}{\frac{33}{48}}\)

= \(\frac{56}{33}\)