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

Explanation

cos x\(\frac{12}{13}\)

13² = 12² + a²

169 = 144 + a²

a² = 169 - 144

a² = 25

a \(\sqrt{25}\)

a = 5

tan x = \(\frac{5}{12}\)

\(\frac{1 - \tan x}{\tan x} = \frac{1 - \frac{5}{12}}{\frac{5}{12}}\)

\(\frac{\frac{1 - \frac{5}{12}}{12 - 5}}{12} = \frac{\frac{7}{12}}{\frac{5}{12}}\)

= \(\frac{7}{2} \div \frac{5}{12}\)

= \(\frac{7}{12} \times \frac{12}{5} = \frac{7}{5}\)