Posted by **Emily** on Monday, April 2, 2012 at 3:57pm.

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

prove the identity

- trig -
**Steve**, Monday, April 2, 2012 at 4:18pm
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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