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 \(\frac{56}{33}\)
waec 2016furthermathematics

The correct answer is D. \(\frac{56}{33}\)

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

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

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

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

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

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