hyperbolic function proof 1

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! boldproof proof

from hyperbolic identity, coshx \cosh{x} = \frac{\exp\^x + \exp\^-x}{2} and sinhx \sinh{x} = \frac{\exp\^x - \exp\^-x}{2} lets add \coshx \coshx + \sinhx \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 \coshx - \sinhx \sinhx = \frac{\exp\^x + \exp\^-x}{2} - \frac{\exp\^x - \exp\^-x}{2} = \frac{2\( exp\^-x ) = bold \exp\^-x then lets multiplty =\coshx \coshx + \sinhx \sinhx * \coshx \coshx - \sinhx \sinhx
= \exp\^x * \exp\^-x = \exp\^x * \frac{1}{\exp\^x} =bold11 so guys, i hope you enjoyed this? like and share! :)

Note by Samuel Ayinde
5 years, 5 months ago

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