# Prove that: (sin θ – 2 sin3 θ) = (2cos3 θ – cos θ) tan θ.

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.

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