math

Rewrite the expression as an algebraic expresion in x:

tan(sin−1x)=

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  1. sorry I meant tan(sin^-1 x)=

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  2. sin^-1 x is angle in a right - angled triangle where the opposite side is x and the hypotenuse is 1
    let that angle be Ø
    so really sin^-1 x ----> sinØ = x/1
    so the third side is √(1 - x^2)

    then tan(sin^-1 x)
    = tan Ø
    = x/√(1-x^2)

    check:

    e.g. let x = .5
    then sin^-1 (.5) = π/6
    and tan(π/6) = .57735

    according to my answer
    tan(sin^-1 (.5)) = .5/√(1-.25) = .57735
    all looks good.

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