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    Question

    If tanθ = (2/√5), then find the value of

    cos2 θ
    A 5/9 Correct Answer Incorrect Answer
    B 5/8 Correct Answer Incorrect Answer
    C 3/5 Correct Answer Incorrect Answer
    D 9/16 Correct Answer Incorrect Answer

    Solution

    Since, sec2 θ - tan2 θ = 1 Therefore, sec2 θ = 1 + (2/√5)2 = {(5 + 4)/5} = (9/5) Therefore, cos2 θ = (1/sec2 θ) = (5/9) Alternate Solution Given, tan θ = (2/√5) = (perpendicular/base) So, perpendicular = 2 units Base = √5 units So, hypotenuse =  √{(22 + ( √ 5)2} =  √(4 + 5) = 3 units So, cos2 θ = (Base/hypotenuse) = (√5/3)2 = (5/9)

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