Given that x = \; 5/12, and y = \; 3/4, Find (x + y).

Correct Answer is : 5633\;56/333356

Correct Answer is : 5633\;56/333356

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WAEC Further Mathematics 2016 Paper

Question : 22

Total: 40

Given that

\tan x = \; \frac{5}{12}

\tan y = \; \frac{3}{4}

\tan (x + y)

Solution:

Concept:

Use the compound angle formula for tangent.

Explanation:

The formula is:

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

Given:

\tan x = \frac{5}{12}, \quad \tan y = \frac{3}{4}

Substitute these values into the formula:

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

Add the fractions in the numerator:

\frac{5}{12} + \frac{3}{4} = \frac{5}{12} + \frac{9}{12} = \frac{14}{12} = \frac{7}{6}

Multiply in the denominator:

\frac{5}{12} \times \frac{3}{4} = \frac{15}{48} = \frac{5}{16}

So the denominator becomes:

1 - \frac{5}{16} = \frac{11}{16}

Therefore:

\tan (x + y) = \frac{\frac{7}{6}}{\frac{11}{16}} = \frac{7}{6} \times \frac{16}{11} = \frac{112}{66} = \frac{56}{33}

Answer:

\frac{56}{33}

Option D.

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