Eh guy, i decided to create this note to prove some hyperbolic identity......
Enjoy...
A famous hyperbolic equation that we all know is:
\( \cosh\^2{x} \)- \( \sinh\^2{x} \)=1
have you ever imagined how this was proved?
lets take a look at it!
*bold*\( proof \)

from hyperbolic identity,
\( \cosh{x} \)= \( \frac{\exp\^x + \exp\^-x}{2} \)
and
\( \sinh{x} \)= \( \frac{\exp\^x - \exp\^-x}{2} \)
lets add
\( \coshx \)+ \( \sinhx \) =\( \frac{\exp\^x + \exp\^-x}{2} \) + \( \frac{\exp\^x - \exp\^-x}{2} \)
using method of L.C.M,
= \( \frac{2\( exp\^x \) )
= *bold*\( \exp\^x \)
now lets subtract,
\( \coshx \)- \( \sinhx \)
=\( \frac{\exp\^x + \exp\^-x}{2} \)
- \( \frac{\exp\^x - \exp\^-x}{2} \)
= \( \frac{2\( exp\^-x \) )
= *bold*\( \exp\^-x \)
then lets multiplty
=\( \coshx \)+ \( \sinhx \) * \( \coshx \)- \( \sinhx \)

= \( \exp\^x \) * \( \exp\^-x \)
=\( \exp\^x \) * \( \frac{1}{\exp\^x} \)
=*bold*\(1\)
so guys, i hope you enjoyed this?
like and share! :)

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