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=4cosx 3(2sinxcosx)=4cosx 6sinxcosx=4cosx 6sinxcosx4cosx=0 2cosx( 3sinx2 )=0 2cosx=0 cosx=0 x= 90 o ,  270 o 3sinx2=0 3sinx=2 sinx= 2 3 x= sin 1 2 3 x= 41.81 o , (18 0 o 41.81 o ) x= 41.81 o , 138 .19 o x= 41.81 o ,  90 o , 138 .19 o ,  270 o


(b)

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

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