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math

cos(arcsin(x)+arctan(x))

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  1. Let arcsin(x) = A
    let arctan(x) = B

    then cos(arcsin(x) + arctan(x))
    = cos(A+B)
    = cosAcosB - sinAsinB **

    from arcsin(x) = A
    sinA = x/1
    cosA = √(1-x^2) , using Pythagoras

    from arctan(x) = B
    tanB = x/1 ,
    then sinB = x/√(x^2 + 1)
    cosB = 1/√(x^2 + 1)

    back into **

    cosAcosB - sinAsinB
    = √(1 - x^2) (1/√(x^2 + 1) - (x/1)(x/√(x^2 + 1)
    = ( √(1 - x^2) - x^2 )/(√(x^2 + 1) )

    check my typing, should have written it out first.

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