Q14 of 123 Page 9

Prove the following identities:

cos3 2x + 3 cos 2x = 4(cos6 x – sin6 x)


Proof:


Take RHS:






{∵ a3 – b3 = (a – b) (a2 + b2 + ab)}



{∵ cos 2x = cos2 x – sin2 x}




{∵ a2 + b2 + 2ab = (a + b)2}



{∵ cos2 x + sin2 x = 1}




{∵ sin 2x= 2 sin x cos x}



{∵ sin2 x = 1 – cos2 x}







= LHS


Hence Proved


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