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

Question

prove the identity

Answer 1

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)