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Prove the Following Identities, Where the Angles Involved Are Acute Angles for Which the Expressions Are Defined. - Mathematics

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

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

 

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Solution

L.H.S

= (sintheta - 2sin^3theta)/2cos^3theta - cos theta

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

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

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

=tan theta = R.H.S

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