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Pre-Calc/Math

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Prove Identity: (1-cos2x/ tan x) = sin2x

  • Pre-Calc/Math - ,

    I think the parentheses are in the wrong place. It should probably read:

    (1-cos2x)/tan x = sin2x

    Again, split everything into sin and cos, and don't forget the identities:
    cos(2x)=cos²(x)-sin²(x)
    sin(2x)=2sin(x)cos(x)

    (1-cos(2x))/tan(x)
    =(1-(cos²(x)-sin²(x))*(cos(x)/sin(x))
    =(1-(1-2sin²(x))*cos(x)/sin(x)
    =2sin²(x)*cos(x)/sin(x)
    =2sin(x)cos(x)
    =sin(2x)

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