We can write the expression sin(x+y) in terms of sinx, cosx, siny and cosy if we use the addition formula for sine,
In turn, it is possible to express the factors cosx and cosy in terms of sinx and siny by using the Pythagorean identity,
Because x and y are angles in the first quadrant, cosx and cosy are positive, so we in fact have
Finally, we obtain