Answer :

To Prove:

Taking LHS,


…(i)


We know that,


a3 – b3 = (a – b)(a2 + ab + b2)


So, cos3x – sin3x = (cosx – sinx)(cos2x + cosx sinx + sin2x)


So, eq. (i) becomes



= cos2x + cosx sinx + sin2x


= (cos2x + sin2x) + cosx sinx


= (1) + cosx sinx [ cos2 θ + sin2 θ = 1]


= 1 + cosx sinx


Multiply and Divide by 2, we get




[ sin 2x = 2 sinx cosx]


= RHS


LHS = RHS


Hence Proved


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