SPM 2020 Add Maths Paper 2, Question 10Trigonometric Functions

Solved on video in English and Bahasa Melayu · Form 5, Trigonometric Functions · 6:20 video

The question

(a)

(a) Prove that (cos 2x + 2 sin x - 1)/(cos x - (1/2) sin 2x) = 2 tan x.

(b)(i)

(b)(i) Hence, sketch the graph of y = (cos 2x + 2 sin x - 1)/(cos x - (1/2) sin 2x) - 1/2 for 0 degrees <= x <= 360 degrees.

(b)(ii)

(b)(ii) Hence, solve the equation (cos 2x + 2 sin x - 1)/(cos x - (1/2) sin 2x) = cos(x/2)/sin(x/2) for 0 degrees <= x <= 180 degrees.

Step 1

Numerator: cos 2x + 2 sin x - 1. Use cos 2x = 1 - 2 sin² x:

Why this step

cos 2x has three forms. Pick 1 − 2 sin²x: the 1 cancels the −1, leaving only sin x. The wrong identity is a common slip.

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

Final answer

Proved

Where students lose marks

Watch out: use cos 2x = 1 − 2 sin²x, and −(1/2) sin 2x becomes −sin x cos x, not −sin x.

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

Final answer

Sketch (see video)

Where students lose marks

Watch out: draw the asymptotes at x = 90° and 270°, and sketch enough of the curve (at least about 1.5 cycles).

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

Final answer

x = 48.18 degrees (only solution in 0 to 180 degrees)

Where students lose marks

Watch out: the left side is 2 tan x, not tan x, and reject the negative root of tan(x/2) for this domain.

Watch every step of this question solved on video (6:20), with the reason behind each step and a box that checks your own answer.

No card. Every past-year question on video, in English and BM.