Trig Functions and Hyperbolic Trig Functions

$$\cos (x) = \frac{e^{ix}+e^{-ix}}{2}$$
$$\sin (x) = \frac{e^{ix}-e^{-ix}}{2i}$$
$$\cos^2(x)+\sin^2(x)=1$$
From this we get:
$$\cos^2(x)+\csc^{-2}(x)=1$$
$$1+\tan^2(x)=\cos^{-2}(x)$$
$$1+\tan^2(x)=\sec^2(x)$$

$$\cosh (x) = \frac{e^{x}+e^{-x}}{2}$$
$$\sinh (x) = \frac{e^{x}-e^{-x}}{2}$$
$$\cosh^2(x)-\sinh^2(x)=1$$

At the moment, this post is incomplete.