nilai x yang memenuhi persamaan sin 3x+sinx = 2cosx untuk 0<=x<=π/2 adalah...

Sin 3x + sin x = 2 cos x
2 sin (3x + x)/2 cos (3x - x)/2 = 2 cos x
2 sin 2x cos x = 2 cos x
Sin 2x cos x = cos x
Sin 2x cos x - cos x = 0
Cos x (sin 2x - 1) = 0
1) cos x = 0
=> cos x = cos 90°
=> x = 90° = π/2

2) (sin 2x - 1) = 0
=> sin 2x = 1
=> sin 2x = sin 90°
=> 2x = 90°
=> x = 45° = π/4

semangat ^_^
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