Given Identity \ \

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 cot θ - tan  = \

    cos2θ     \ \   sinθ cosθ

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Start from Left Hand Side(LHS) \ \

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cot θ - tan θ

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cosθ \ \ sinθ \ \ \

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sinθ \ \ cosθ \ \

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Rewrite the expression with common denominator. \ \

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cos²θ - sin²θ \ \   cosθsinθ \ \

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Substitute formula : cos²θ - sin²θ = cos 2θ \ \

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    cos2θ     \ \   sinθ cosθ

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Given Identity Cot θ − tan θ = cos 2θ/(sin θ cos θ) is proved \ \