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Question
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
Solution
2 sin A − 1 = 0
`=> sin A = 1/2`
We know `sin 30^circ = 1/2`
So, A = 30°
L.H.S. = sin 3 A = sin 90° = 1
R.H.S. = 3 sin A – 4 sin3 A
= 3 sin 30° – 4 sin3 30°
= `3(1/2) - 4(1/2)^3`
= `3/2 - 1/2`
= 1
L.H.S. = R.H.S.
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