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    Question

    If cos – sin θ = √2 sin θ, then (cos θ + sin θ)

    is:
    A –√2 cos θ Correct Answer Incorrect Answer
    B √2 cos θ Correct Answer Incorrect Answer
    C √2 tan θ Correct Answer Incorrect Answer
    D –√2 sin θ Correct Answer Incorrect Answer

    Solution

    Given, cos θ -sin θ = √2 sin θ square both sides, we get. Cos2 θ + sin2 θ -2 sin θ cos θ =2 sin θ   1- 2sin θ. cos θ = 2sin2 θ = 2 sin θ cos θ = 1-2 sin² θ .... (i) Now, consider cos θ + sin θ.   By Squaring this expression, we get (cos θ + sin θ)2 = cos2 θ + sin2 θ + 2 sin θ cos θ =1+1-2sin2 θ = 2-2sin2 θ = 2(1 – sin2 θ)   = 2cos2 θ   cos θ + sin θ = √2 cos θ

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