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    Question

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    A cosecθ secθ Correct Answer Incorrect Answer
    B -1 Correct Answer Incorrect Answer
    C 1 Correct Answer Incorrect Answer
    D sinθcosθ Correct Answer Incorrect Answer

    Solution

    = sin θ[(1 - tan θ) tan θ + sec2 θ] / (1 - sin θ)(tan θ)(1 + tan θ)(sec θ + tan θ) = sin θ[tan θ – tan2 θ + sec2 θ] / 1 - sin θ) (sin θ / cos θ) ( 1 + tan θ)(1 + sin θ / cos θ) = [tan θ + 1] / 1 – sin2 θ (1 + tan θ)1/cos2 θ = cos2 θ / cos2 θ = 1 Using (1 – sin θ)(1 + sin θ) = 12 – sin2 θ (a + b)(a – b) = a2 – b2

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