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L.H.S = cos3A = cos(2A+A) = cos2A.cosA – sin2A.sinA = (2cos2A - 1)cosA – 2sinA cosA sinA = 2cos3A – cosA – 2cosA(1-cos2A) = 2cos3A – cosA – 2cosA + 2cos3A = 4cos3A – 3cosA = R.H.S.Read more on Sarthaks.com - https://www.sarthaks.com/605035/prove-that-cos3a-4cos-3a-3cosa?show=605043#a605043
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