Home » » 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) $$\frac{13}{5}$$

### Explanation:

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

## 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 = $$\frac{5}{12}$$
$$\frac{1 - \tan x}{\tan x} = \frac{1 - \frac{5}{12}}{\frac{5}{12}}$$
$$\frac{\frac{1 - \frac{5}{12}}{12 - 5}}{12} = \frac{\frac{7}{12}}{\frac{5}{12}}$$
= $$\frac{7}{2} \div \frac{5}{12}$$
= $$\frac{7}{12} \times \frac{12}{5} = \frac{7}{5}$$