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Prove that cos3A = 4cos^3A - 3cosA.

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Prove that cos3A = 4cos3A - 3cosA.

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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.

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