Q21 of 123 Page 9

Prove the following identities:

cos6 x – sin6 x = cos 2x


Proof:


Take LHS:



Identities used:


(a + b)2 = a2 + b2 + 2ab


a3 – b3 = (a – b) (a2 + b2 + ab)


Therefore,




{∵ cos 2x = cos2 x – sin2 x}




{∵ sin2 x + cos2 x = 1}



{∵ sin 2x = 2 sin x cos x}




= RHS


Hence Proved


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