WAEC Mathematics 2014 Paper

Concept:Use the given $\cos x$ to find $\tan x$ from a right triangle, then simplify the expression.Explanation:Given $\cos x = \frac{12}{13}$.In a right triangle, $\cos x = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{13}$.Let the opposite side be $a$.By Pythagoras theorem: $13^2 = 12^2 + a^2$.So $169 = 144 + a^2$.$a^2 = 25$.$a = 5$.Thus $\tan x = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{12}$.Substitute into the given expression:$\frac{1 - \tan x}{\tan x} = \frac{1 - \frac{5}{12}}{\frac{5}{12}}$.Simplify the numerator: $1 - \frac{5}{12} = \frac{7}{12}$.So the expression becomes $\frac{\frac{7}{12}}{\frac{5}{12}}$.Dividing by a fraction means multiplying by its reciprocal:$\frac{7}{12} \times \frac{12}{5} = \frac{7}{5}$.Answer:$\frac{7}{5}$This is Option C.