Given that \(\tan x = \frac{5}{12}\), and \(\tan y = \frac{3}{4}\), Find \(\tan (x +
FURTHER MATHEMATICS
WAEC 2016
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: D. \(\frac{56}{33}\)
Explanation
\(\tan (x + y) = \frac{\tan x + \tan y}{1 - \tan x\tan y}\)
\(\tan x = \frac{5}{12} ; \tan y = \frac{3}{4}\)
\(\tan (x + y) = \frac{\frac{5}{12} + \frac{3}{4}}{1 - (\frac{5}{12} \times \frac{3}{4}})\)
= \(\frac{\frac{14}{12}}{\frac{33}{48}}\)
= \(\frac{56}{33}\)
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