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Which one of the following is NOT a correct identity?

Competition practiceTrigonometry
  • Asin2θ = 2sinθ·cosθ
  • Bcos2θ = 1 − 2siθ
  • Ctan2θ = 2tanθ/(1 + taθ)
  • Dcot2θ = (coθ − 1)/(2cotθ)

Step-by-Step Solution

The correct double-angle tangent has 1 − taθ downstairs; 2tanθ/(1 + taθ) is sin2θ, so the two formulas have been crossed. Test at θ = 23°: 2tan23°/(1 + ta23°) = 0.719, which is sin46°, while tan46° = 1.036. The other three are standard, including cot2θ = (coθ − 1)/(2cotθ), which at θ = 23° gives 0.966 = cot46°.
Answer: C) tan2θ = 2tanθ/(1 + taθ)

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