Home » Past Questions » Mathematics » Given that cos x = \(\frac{12}{13}\), evaluate \(\frac{1 - \tan x}{\tan x}\)

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


Question

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

Options

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

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

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

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

The correct answer is 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 = \(\frac{5}{12}\)
\(\frac{1 - \tan x}{\tan x} = \frac{1 - \frac{5}{12}}{\frac{5}{12}}\)
\(\frac{\frac{1 - \frac{5}{12}}{12 - 5}}{12} = \frac{\frac{7}{12}}{\frac{5}{12}}\)
= \(\frac{7}{2} \div \frac{5}{12}\)
= \(\frac{7}{12} \times \frac{12}{5} = \frac{7}{5}\)


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Dicussion (1)

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