Prove each of the following identities:
Consider L.H.S. =
Using identities (a3 + b3) = (a + b)(a2 + b2 – ab) and (a3 – b3) = (a – b)(a2 + b2 + ab)
∴ L.H.S. =
= (cos2 θ + sin2 θ – cos θ sin θ) + (cos2 θ + sin2 θ + cos θ sin θ)
= (1 – cos θ sin θ) + (1 + cos θ sin θ)
= 2
= R.H.S.
Hence, proved.