Write an algebraic expression for the following:

Question

sin⁡(arctan⁡〖(x+1)/(x-1)〗 )

Answer 1

draw your triangle. If the legs of the triangle are x+1 and x-1, the hypotenuse is √((x+1)^2 + (x-1)^2)) = √(2x^2+2)

so, sin(arctan((x+1)/(x-1)) = (x+1)/√(2x^2+2)