Prove that
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