Given that cos x = (frac{12}{13}), evaluate (frac{1 – tan x}{tan x})

Correct Answer: Option C

Explanation

cos x(frac{12}{13})
13² = 12² + a²
169 = 144 + a²
a² = 169 – 144
a² = 25
a (sqrt{25})
a = 5
tan x = (frac{5}{12})
(frac{1 – tan x}{tan x} = frac{1 – frac{5}{12}}{frac{5}{12}})
(frac{frac{1 – frac{5}{12}}{12 – 5}}{12} = frac{frac{7}{12}}{frac{5}{12}})
= (frac{7}{2} div frac{5}{12})
= (frac{7}{12} times frac{12}{5} = frac{7}{5})