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SPM 2021 Add Maths Trial Paper (Selangor) – Paper 1 (Question 14)


Question 14:
(a) Solve the equation 3 sin⁡ 2x = 4 cos⁡x for 0 ≤ x ≤ 360. [4 marks]
(b) Solve the simultaneous equations 2 cos⁡ (xy) = √3 and 2 cos ⁡(x + y) = 1, where x and y are both acute angles. [4 marks]

Solution:
(a)

3sin2x=4cosx3(2sinxcosx)=4cosx6sinxcosx=4cosx6sinxcosx4cosx=02cosx(3sinx2)=02cosx=0cosx=0x=90o, 270o3sinx2=03sinx=2sinx=23x=sin123x=41.81o, (180o41.81o)x=41.81o, 138.19ox=41.81o, 90o, 138.19o, 270o


(b)

2cos(xy)=3cos(xy)=32(xy)=cos1(32)(xy)=30 ….. (1)2cos(x+y)=1cos(x+y)=12(x+y)=cos1(12)(x+y)=60 ….. (2)xy=30 ….. (1)x+y=60 ….. (2)(1)+(2),2x=90x=45From (1),45y=30y=15

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