Question

can someone please explain this trig identity (?)

Answer 1

\[\cos(\arcsin \sqrt{x})=\sqrt{1-x}\]

Answer 2

arcsin sqrtx means the angle whose sine is sqrtx

and sqrt(1-x) is the cosine of this angle

this arises from the identity sin^2 x + cos ^2 x = 1
cos x = sqrt ( 1 - sin^2 x)

Answer 3

and if sin x = sqrtx

then cos x = sqrt(1 - (sqrtx)^2) = sqrt ( 1 - x)

Answer 4

oohh I see. thanks!