Posted by **jh** on Monday, March 22, 2010 at 4:05am.

Can anyone help me with this question please!!

Show that

(cosh x)^2 - (sinh x)^2 = 1

for every real number x.

- Precalculus -
**MathMate**, Monday, March 22, 2010 at 8:24am
Expand and simplify using:

cosh(x)=(e^{x}+e^{-x})/2

sinh(x)=(e^{x}-e^{-x})/2

noting that e^{x} * e^{-x}=1

For the domain, since both e^{x} and e^{-x} have a domain of R, so the expression cosh(x)²-sinh(x)²=1

also has a domain of R, or (-∞,&infin).

## Answer this Question

## Related Questions

- Maths - use the formula cos(x+iy)=cosxcosiy-sinxsiniy to find two imaginary ...
- maths 2 - The original question I had was write arcsin4 in the form a+ib. I ...
- calculus - what is the anti-derivative on square root of cosh^2(x)? The square ...
- calc: arc length - find the exact length of this curve: y = ( x^3/6 ) + ( 1/2x...
- Calculus - so we are doing integrals and I have this question on my assignment ...
- Calculus - Solve the differential equation. Let C represent an arbitrary ...
- 7th grade math ms.sue - 4. Which statement is true? (1 point) Every real number ...
- Calculus - Find the derivatives of the function f(t)=cosh^2(4t)-sinh^2(4t). ...
- Math - Which statement is false? A. Every integer is a real number*** B. The ...
- Math - which statement is false?(1 point) a.every integer is a real number b.the...

More Related Questions