Question

prove: sinh^2(x)=-1+cosh(2x)/2

Answer 1

So convert to exponentials and work it out! :)\[\Large\rm \sinh^2x=\left[\frac{1}{2}(e^x-e^{-x})\right]^2\]

Answer 2

\[\Large\rm \frac{1}{4}(e^x-e^{-x})^2\]Understand how to expand that binomial out?

Answer 3

no really. my teacher gave me an example and it has my head swimming.

Answer 4

So recall how we expand a square binomial:\[\Large\rm (a-b)^2=a^2-2ab+b^2\]It's the square of the first, the square of the second, and also 2 times the product of both.

Answer 5

\[\Large\rm (e^x-e^{-x})^2=(e^x)^2-2e^x e^{-x}+(e^{-x})^2\]

Answer 6

Then we need to use rules of exponents to simplify the squares.
Recall your exponent rule:\[\Large\rm (a^b)^c=a^{bc}\]

Answer 7

okay