Rewrite the expression as an algebraic function of x and y.

Question

cos(sin^-1(x)-tan^-1(y))

Answer 1

Let A = sin^-1x. Then sinA = x and cosA = √[1-sin²A] = √[1-x².]

Let B = tan^-1y. Then tanB = y = y/1. So, cosB = 1/√[1+y²] and sinB = y / √[y²+1]

cos(sin^-1x - tan^-1y) = cos(A-B) =cosAcosB + sinAsinB =

√[(1-x²) / (1+y²)] + xy / √(1+y²) = [xy + √(1-x²) ] / √(1+y²)