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

A.

\(\frac{5}{13}\)

B.

\(\frac{5}{7}\)

C.

\(\frac{7}{5}\)

D.

\(\frac{13}{5}\)

Correct answer is C

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

132 = 122 + a2

169 = 144 + a2

a2 = 169 - 144

a2 = 25

a \(\sqrt{25}\)

a = 5

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

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

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

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

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