Proving hyperbolic trig formula

[tuly]

hello everyone..could you please help me with these 2:

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

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

 

[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!

 

[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.

 

[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.

 

[tuly]

thanks

thanks for your help...