Finding the Real part of tan(z) or tan(x+iy) Prove that $~\Re\left(\tan(z)\right) =\dfrac{\sin(x)\cos(x)}{\cos^2(x)+\sinh^2(y)}~~$ (where $z=x+iy$)
I have solved for it using trigonometric identities and some simple algebra but I've only reached so far:
$$\Re\left(\tan(z)\right)=\frac{\sin(x)\cos(x)}{\cos^2(x)\cosh^2(y) + \sin^2(x)\sinh^2(y)}$$
And I'm stuck.

Hint Use the Pythagorean Identity $$\cosh^2 y = \sinh^2 y + 1 .$$
