trig

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cos(sin^-1 x)=sq rt(1-x^2)

prove the identity

  • trig -

    draw a triangle with opposite leg=x, hypotenuse=1

    adjacent leg = √(1-x^2)

    however, doing it algebraically,

    let θ=sin^-1 x
    x = sinθ

    cos^2 θ + sin^2 θ = 1
    cos^2 θ + x^2 = 1
    cos^2 θ = 1 - x^2
    cosθ = √(1-x^2)

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