Rewrite the expression as an algebraic function of x and y. cos(sin^−1(x) − tan^−1(y))

Question

I need help rewriting this in terms of x and y

Answer 1

Draw 2 figures, each a right triangle containing angle x and angle y respectively,

then use Pythagorean theorem.

What you want is

cos arcsin x * cos arctan y + sin arcsin x * sin arctan y =

(1/sqrt(1-x²) * (1/sqrt(1+x²) + x * (y/sqrt(1+x²)

and I will leave it to you to collect the terms.