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Question
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
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Solution
4 cos2 A – 3 = 0
`=>` 4 cos2 A = 3
`=> cos^2A = 3/4`
`=> cosA = sqrt3/2`
We know cos 30° `= sqrt(3)/2`
So, A = 30°
L.H.S. = cos3 A = cos 90° = 0
R.H.S. = 4 cos3 A – 3 cos A
= 4 cos3 30° – 3 cos 30°
= `4(sqrt3/2)^3 - 3(sqrt3/2)`
= `(3sqrt3)/2 - (3sqrt3)/2`
= 0
L.H.S. = R.H.S.
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