inverse trigonometry

put cos^-1 x/a = α1  and cos^-1y/b=α2

so α₁+α₂=α   and cos α₁ =x/a  and cosα₂ = y/b

now cos(α₁+α₂)= cosα₁*cosα₂ - sinα₁*sinα₂ = cosα

or     cosα₁*cosα₂-cosα=sinα₁*sinα₂

square both the sides and replace the values

sinα₁ = ( 1- cos^₂α₁)^1/2 = (1- (x²/a²))^1/2

sinα₂ = ( 1- cos^₂α₂)^1/2 = (1- (y²/b²))^1/2