# Prove the following identity, where the angles involved are acute angles for which the expressions are defined.(vii) (sintheta-2sin^3theta)/(2cos^3th

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Prove the following identity, where the angles involved are acute angles for which the expressions are defined.
(vii) (sintheta-2sin^3theta)/(2cos^3theta-costheta)=tantheta

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L.H.S. =(sintheta - 2sin^3theta)/(2cos^3theta-costheta)
=(sintheta(1-2sin^2theta))/(costheta(2cos^2theta-1))
=tantheta(cos^2theta+sin^2theta-2sin^2theta)/(2cos^2theta-cos^2theta-sin^2theta)
=tantheta(cos^2theta-sin^2theta)/(cos^2theta-sin^2theta)
=tantheta=R.H.S.`