SPM 2022 Add Maths Paper 2, Question 6Trigonometric Functions

Solved on video in English and Bahasa Melayu · Form 5, Trigonometric Functions · 6:30 video

The question

(a)

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

(b)

(b) (i) Hence, sketch the graph of y = |cot(x/2) − 2 cot x| − 1 for 0° ≤ x ≤ 360°. (ii) There is no solution obtained if y = m is sketched on the same axes in 6(b)(i), such that m is a constant. State the range of values of m.

SPM 2022 Add Maths Paper 2, Question 6: the question as drawn in Eduly's video6:30

Part (a)

Step 1

LHS = cot(x/2) − tan(x/2) = cos(x/2)/sin(x/2) − sin(x/2)/cos(x/2).

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

Final answer

Proved

Where students lose marks

Watch out: use the double-angle formulas with θ = x/2 and carry on to 2 cot x. Don't stop at renaming x/2 = A.

Part (b)

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

Final answer

(i) Sketch (see video); (ii) m < −1

Where students lose marks

Watch out: on 0° to 360° there is only one asymptote, at x = 180°. Extra asymptotes lead to the wrong range of m.

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