Question

Prove that \( \cos \left(\sin^{-1} u\right) = \sqrt{1-u^2} \)

Answer 1

let sin inverse u = theta
thus sin theta = u
by taking theta as an angle we can draw a right angled triangle whose perpendicular is u and hypotenuse is 1

Answer 2

using pythagorean theorem base will be square root of 1 - u square

Answer 3

and cos theta = square root of 1 - u square

Answer 4

or theta = cos inverse (\[\sqrt{1-u \square}\]