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Prove the following identities, where the angles involved are acute angles for which the expressions are defined

`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`

Prove that `(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`

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#### Solution

L.H.S = `(sin theta-2sin^3theta)/(2cos^3theta -costheta)`

`= (sintheta(1-sin^2theta))/(costheta(2cos^2theta-1))`

`= (sinthetaxx(1-2sin^2theta))/(costhetaxx{2(1-sin^2theta)-1})`

`= (sin thetaxx(1-2sin^2theta))/(costhetaxx(1-2sin^2theta))`

= `tantheta` = R.H.S

Concept: Trigonometric Identities

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