ProofHard4 marks
Prove that (sin θ - 2sin³ θ) / (2cos³ θ - cos θ) = tan θ
Topic: Trigonometric identities
Previous-year question practice database
Answer
Exam answer
Left-hand side = (sinθ − 2sin³θ)/(2cos³θ − cosθ)
= sinθ(1−2sin²θ) / [cosθ(2cos²θ−1)].
Using sin²θ+cos²θ=1: 1−2sin²θ = cos²θ−sin²θ, 2cos²θ−1 = cos²θ−sin²θ.
Therefore: Left-hand side = sinθ/cosθ = tanθ = Right-hand side.
Hence proved.
Explanation
Factor sinθ and cosθ and use sin²θ+cos²θ=1 to obtain the same common factor in numerator and denominator.
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