Question

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`

Answer 1

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