# Proving hyperbolic trig formula

1. Sep 2, 2005

### tuly

cosh^2 X=(cosh (2X)+1)/2

sinh(X+Y)=sinh X.cosh Y+cosh X.sinh Y

2. Sep 2, 2005

### da_willem

How about using the definitions of cosh and sinh in terms of exponentials and use some standard rules for exponents? Show your work!

3. Sep 2, 2005

### Curious3141

Even easier : what relationships do you know between the usual trigonometric functions of imaginary variables and the hyperbolic trig functions of those variables ? The problem can be reduced to simple compond angle trig.

4. Sep 2, 2005

### amcavoy

Here it is for circular trig. functions:

$$\cos{2x}=\cos^2{x}-\sin^2{x}=2\cos^2{x}-1$$

From here, you can solve for $\cos^2{x}$ and you will have your answer for circular functions. Now, apply this to hyperbolic functions.

5. Sep 3, 2005

thanks