Consider R.H.S. = (2cos³ θ – cos θ) tan θ

= cos θ(2cos² θ – 1)

= (2cos² θ – 1)sin θ

Consider L.H.S. = (sin θ – 2 sin³ θ)

= sin θ(1 – 2 sin² θ)

= sin θ[1 – 2(1 – cos² θ)]

= sin θ [1 – 2 + 2cos² θ]

= sin θ (2cos² θ – 1)

Therefore, L.H.S. = R.H.S.

Hence, proved.