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Question
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Solution
LHS = `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ)`
= `(sin θ(1 - 2sin^2 θ))/(cos θ(2 cos^2 θ - 1))`
= `(tan θ(1 - 2(1 - cos^2 θ)))/(2 cos^2θ - 1 )`
= `(tan θ(1 - 2 + 2 cos^2 θ))/(2 cos^2θ - 1 )`
= `(tan θ(2 cos^2 θ - 1))/(2 cos^2θ - 1 )`
= tan θ
= RHS
Hence proved.
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