WAEC 2019 Mathematics · Question 50

If tan x = $\frac{3}{4}$ , 0 < x < 90 $^o$ , evaluate $\frac{\cos x}{2 sin x}$

Options

A. $\frac{8}{3}$
B. $\frac{3}{2}$
C. $\frac{4}{3}$
D. $\frac{2}{3}$

Answer: D. $\frac{2}{3}$

Explanation written with AI and checked against the answer key

Analyze the question: We're given tan x = 3/4 and must find cos x / (2 sin x). Concept: cos x / sin x = cot x = 1/tan x. Solution: cos x / (2 sin x) = (1/2) × (cos x / sin x) = (1/2) × (1/tan x) Substitute tan x = 3/4: 1/tan x = 4/3 So (1/2) × (4/3) = 4/6 = 2/3 Check with the 3-4-5 triangle: opposite = 3, adjacent = 4, hypotenuse = 5. sin x = 3/5, cos x = 4/5. cos x / (2 sin x) = (4/5) / (6/5) = 4/6 = 2/3 ✓ Answer: D (2/3) Tip: When you see cos/sin, think "cot", which is the reciprocal of tan. Pull out the constant (the 2 in the denominator) first, then flip tan. Option C (4/3) is the trap for students who forget the factor of 2.

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If tan x = 34\frac{3}{4}43​, 0 < x < 90o^oo, evaluate cos⁡x2sinx\frac{\cos x}{2 sin x}2sinxcosx​

Options

Answer: D. 23\frac{2}{3}32​

If tan x = $\frac{3}{4}$ , 0 < x < 90 $^o$ , evaluate $\frac{\cos x}{2 sin x}$

Answer: D. $\frac{2}{3}$