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    Question

    If 5tanθ = 12, then find the value of (sinθ –

    cosθ).
    A 12/13 Correct Answer Incorrect Answer
    B 7/13 Correct Answer Incorrect Answer
    C 5/13 Correct Answer Incorrect Answer
    D None of these Correct Answer Incorrect Answer

    Solution

    We have, 5tanθ = 12

    So, tan θ = (12/5)

    Or, (perpendicular/base) = (12/5)

    So, hypotenuse 2  = base 2  + perpendicular 2  = 5 2  + 12 2

    So, hypotenuse = √169 = 13

    So, sin θ = (perpendicular/hypotenuse) = (12/13)

    And, cos θ = (base/ hypotenuse) = (5/13)

    Therefore, sin θ – cos θ = (12/13) – (5/13) = (7/13)

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