Melaka Trial 2025 Add Maths Paper 2, Question 10Trigonometric Functions

Solved on video in English · Form 5, Trigonometric Functions · 7:47 video

The question

(a)

(a) Prove that cot x − tan x = 2 / tan 2x.

(b)

(b) Hence, solve the equation cot x − tan x = 3 for 0° ≤ x ≤ 360°.

(c)(i)

(c)(i) Sketch the graph of y = −2 sin (3x/2) + 1 for 0° ≤ x ≤ 2π.

(c)(ii)

(c)(ii) There is one solution obtained if y = t is drawn on the same axes as in 10(c)(i), where t is a constant. State the value of t.

Melaka Trial 2025 Add Maths Paper 2, Question 10: the question as drawn in Eduly's video7:47

Part (a)

Step 1

Write in terms of sin and cos: cot x − tan x = cos x/sin x − sin x/cos x.

Why this step

cot and tan are both built from sin and cos, so writing them this way lets us combine everything into one fraction and spot the double-angle patterns.

3 more steps, each with the reason for it, in the full solution

Final answer

Proven

Where students lose marks

Watch out: learn cos²x − sin²x = cos 2x and 2 sin x cos x = sin 2x, and end at 2 / tan 2x.

Part (b)

5 more steps, each with the reason for it, in the full solution

Final answer

x = 16.85°, 106.85°, 196.85°, 286.85°

Where students lose marks

Watch out: 2x runs from 0° to 720°, so list all four values of 2x before dividing by 2.

Part (c)(i)

4 more steps, each with the reason for it, in the full solution

Final answer

Sketch (see video)

Where students lose marks

Watch out: 1½ cycles in 0 to 2π, a reflection for −2, and a shift up 1, so max 3 and min −1.

Part (c)(ii)

3 more steps, each with the reason for it, in the full solution

Final answer

t = 3

Where students lose marks

Watch out: t = −1 touches the curve twice, so it gives two solutions. Only the maximum, t = 3, is touched exactly once.

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