stuck on hyperbolic functions?

Question

hey i'm stuck on this question:
i have to use the definitions of hyperbolic functions to show that cosh^2x = 1/2(cosh 2x + 1)

i assume that means i have to use
cosh^2 x - sinh^2 x = 1
sinh(x +/- y) = sinh x cosh y +/- cosh x sinh y
cosh (x +/- y) = cosh x cosh y +/- sinh x sinh y

so can anybody show me step by step what to do?
just a final answer is no good to me, i need to understand this.
cheers.

Answer 1

Put x=y in your third formula, to give
cosh 2x = cosh(^2) x + sinh(^2) x. and match this against
1 = cosh(^2) x - sinh(^2) x.

If you add left and right hand sides, what do you get?

Answer 2

you could use the definition of cosh x =(e^x+e^-x)/2
so ( coshx)^2=(e^2x+e^-2x+1)/4 = 1/2[(e^2x+e-^2x)/2 +1/2 ]
but (e^2x+e^-2x)/2 is cos h 2x so you got your formula