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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! 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! :)

Note by Samuel Ayinde
3 years, 4 months ago

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