Rewrite the expression as an algebraic function in x and y. cos(sin^-1(x)+tan^-1(y))

Answer 1

I did it a little different:

Let a = arcsin(x) --> sin(a) = x/1 and cos(a) = √(1-x²)/1

Let b = arctan(y) --> tan(b) = y/1 , sin(b) = y/√(1+y²), cos(b) = 1/√(1+y²)

Using the cosine addition formula

cos(a+b) = cos(a)cos(b) - sin(a)sin(b) = (√(1-x²)/1)(1/√(1+y²)) - (x/1)(y/√(1+y²))

f(x,y) = (√(1-x²) - xy) / √(1+y²)

Answer 2

Create 2 figures with each being a right triangle and having angle x and y respectively. After doing so, employ Pythagorean theorem.

Ultimately, you will receive...

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)

This is the first of many steps, so continue on from here and be sure to have your answer in terms of x and y.

Cheers!