Hyperbolic functions

[Rokpaperatombom]

Working through some uni work and it asks me to prove cosh2x=1+2sinh^2x

Would someone be able to show me how to do it step by step please. Tia

 

[Deleted member 4993]

Working through some uni work and it asks me to prove cosh2x=1+2sinh^2x

Would someone be able to show me how to do it step by step please. Tia

First thing you have to tell us:

How would you define cosh(x)?​

 

[Rokpaperatombom]

Cosh(x)=(e^x+e^-x)/2

 

[Steven G]

It follows from the definitions so answer Subhotosh Khan's question.

 

[Deleted member 4993]

Cosh(x)=(e^x+e^-x)/2

Then continue ..... How would you define cosh(2x)? [or is it cosh²(x)]

 

[Rokpaperatombom]

Then continue ..... How would you define cosh(2x)? [or is it cosh²(x)]

Cosh(2x)=(e^2x+e^-2x)/2

 

[Deleted member 4993]

Then continue ..... How would you define sinh(x)?

Why is it feeing like pulling teeth......

 

[pka]

Working through some uni work and it asks me to prove cosh2x=1+2sinh^2x

Work with these:
\(\begin{gathered}
\cosh (x) = \frac{{{e^x} + {e^{ - x}}}}{2} \hfill \\
\sinh (x) = \frac{{{e^x} - {e^{ - x}}}}{2} \hfill \\
{\sinh ^2}(x) = \frac{{{e^{2x}} - 2 + {e^{ - 2x}}}}{4} \hfill \\
\cosh (2x) = \frac{{{e^{2x}} + {e^{ - 2x}}}}{2} \hfill \\
\end{gathered} \)

 

[Rokpaperatombom]

Thanks for the help guys. I've always lacked confidence when it comes to maths. I think after a long day my brain was just fried. I really appreciate the help

 

[Rokpaperatombom]