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    Question

     If sinθ +cos θ = √5/2, then find the value of

    sinθ – cosθ.
    A 1 Correct Answer Incorrect Answer
    C 1/2 Correct Answer Incorrect Answer
    D √3/2 Correct Answer Incorrect Answer

    Solution

    sinθ +cos θ = √5/2, Squaring both sides.   sin2θ + cos2θ + 2sinθ .cosθ = 5/4  1 + 2sinθ .cosθ = 5/4 sinθ .cosθ = 1/8 We can write; sin2θ + cos2θ = (sinθ – cosθ)2 + 2sinθ.cosθ   (sinθ – cosθ )2 = 1 – 1/4 = 3/4 (sinθ – cosθ ) = √3 /2

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