Calc- prove sinh(x) and cosh(x) identities?

[J.live]

Homework Statement

Prove

cosh(2x)= cosh^2(x) + sinh^2(x)

Homework Equations

sinh(x) ≡ [ e^(x) - e^(-x) ] / 2

cosh(x) ≡ [ e^(x) + e^(-x) ] / 2

The Attempt at a Solution

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

= [ e^(x) + e^(-x) ]² / 2² + [ e^(x) - e^(-x) ]² / 2²

... gets confusing after this. Thanks in advance.

 

[Mark44]

Homework Statement

Prove

cosh(2x)= cosh^2(x) + sinh^2(x)

Homework Equations

sinh(x) ≡ [ e^(x) - e^(-x) ] / 2

cosh(x) ≡ [ e^(x) + e^(-x) ] / 2

The Attempt at a Solution

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

= [ e^(x) + e^(-x) ]² / 2² + [ e^(x) - e^(-x) ]² / 2²

... gets confusing after this. Thanks in advance.

How is it confusing? All you are doing is expanding the squares of two binomials. You know how to expand (a + b)², right?

 

[kbaumen]

Have you tried expanding the brackets on the numerators?

 

[gomunkul51]

confusing

Not the right attitude ! :)