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Question
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Solution
L.H.S. = `(sintheta - 2sin^3theta)/(2cos^3theta - costheta)`
= `(sintheta(1 - 2sin^2theta))/(costheta(2cos^2theta - 1))`
= `(sintheta(1 - 2sin^2theta))/(costheta[2(1 - sin^2theta) - 1])`
= `(sintheta(1 - 2sin^2theta))/(costheta(2 - 2sin^2theta - 1))`
= `(sintheta(1 - 2sin^2theta))/(costheta(1 - 2sin^2theta))`
= `sintheta/costheta`
= tan θ = R.H.S.
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