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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
2 years, 8 months ago