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: 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 = \(\frac{5}{12}\)
\(\frac{1 - \tan x}{\tan x} = \frac{1 - \frac{5}{12}}{\frac{5}{12}}\)
\(\frac{\frac{1 - \frac{5}{12}}{12 - 5}}{12} = \frac{\frac{7}{12}}{\frac{5}{12}}\)
= \(\frac{7}{2} \div \frac{5}{12}\)
= \(\frac{7}{12} \times \frac{12}{5} = \frac{7}{5}\)
