Question
If tanθ = (2/√5), then find the value of
cos2 θSolution
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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