Tuesday

September 30, 2014

September 30, 2014

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

Show that

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

for every real number x.

- Precalculus -
**MathMate**, Monday, March 22, 2010 at 8:24amExpand 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 - Solve the differential equation. Let C represent an arbitrary ...

Calculus - so we are doing integrals and I have this question on my assignment ...

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). ...

Calculus - Graph the curve and find its exact length. x = e^t + e^-t, y = 5 - 2t...

Math - Find the volume of the solid generated by revolving the region bounded by...