# Prove that</p

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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