WAEC 2014 Mathematics · Question 37

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. $\frac{13}{5}$

Answer: C. $\frac{7}{5}$

Explanation written with AI and checked against the answer key

Analyze the question: We are given cos x = 12/13 and must find (1 − tan x)/tan x. Concept: Use a right-angled triangle, where cos x = adjacent/hypotenuse and tan x = opposite/adjacent. Solution: Adjacent = 12 and hypotenuse = 13, so opposite = √(13² − 12²) = √(169 − 144) = √25 = 5 Therefore tan x = 5/12. Now substitute: (1 − tan x)/tan x = (1 − 5/12)/(5/12) = (7/12)/(5/12) = 7/5 Equivalently, (1 − tan x)/tan x = 1/tan x − 1 = 12/5 − 1 = 7/5. Answer: 7/5, which is option C. Tip: Whenever you see an expression like (1 − tan x)/tan x, split it into 1/tan x − 1 = cot x − 1. This saves time. Also remember the 5-12-13 Pythagorean triple, because it appears often in WASSCE and JAMB questions.

AI can make mistakes. Report anything that looks wrong.

Given that cos x = 1213\frac{12}{13}1312​, evaluate 1−tan⁡xtan⁡x\frac{1 - \tan x}{\tan x}tanx1−tanx​

Options

Answer: C. 75\frac{7}{5}57​

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

Answer: C. $\frac{7}{5}$