Question

If y = sin^-1 [x√(1 - x) - √x√(1 - x²)], find dy/dx.

Answer 1

∵ y = sin^-1 [x√(1 - x) - √x√(1 - x²)]

Putting x = sin θ and √x = sin ϕ

∴ y = sin^-1 [sinθ cosθ - sinϕ cosθ] 

y = sin^-1[sin(θ - ϕ)]

y = θ - ϕ

y = sin^-1 x - sin^-1 √x