# Hyperbolic Trigonometric Identity: cosh(x-y)

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• Published on Feb 22, 2021

In this video I go over another Hyperbolic Trig Identity and this time prove that cosh(x-y) = cosh(x)cosh(y) – sinh(x)sinh(y). This is a very quick proof because I simply use the derivation for cosh(x+y) that I solved in my earlier video, and then simply replace +y with -y. Thus using the definition of cosh and sinh, I show also that cosh(-y) = cosh(y) and sinh(-y) = -sinh(y). Thus the only thing that changes is we get a negative sign added to sinh(y) and thus the formula is identical to the cosh(x+y) identity expect we subtract sinh(x)sinh(y) instead of add. This is a very quick tutorial in proving the identity and I will be using this result in later video so make sure to watch this video!

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/m2tao-video-notes-hyperbolic-trigonometric-identity-cosh-x-y

Related Videos:

Hyperbolic Trigonometric Identity: cosh(x+y): https://youtu.be/B_rfrnhx-t4
Hyperbolic Functions - tanh(x), sinh(x), cosh(x) - Introduction: http://youtu.be/EmJKuQBEdlc
Hyperbolic Trigonometry Identity Proof: sinh(x+y) = sinh(x)cosh(y) + cosh(x)sinh(y): http://youtu.be/hrOId-Yp2rk
Hyperbolic Trigonometry Identity Proof: cosh(x+y) = cosh(x)cosh(y) + sinh(x)sinh(y): http://youtu.be/UEHQ8SSqDXc
Hyperbolic Trigonometry Identity Proof: sinh(-x) = -sinh(x), cosh(-x) = cosh(x): http://youtu.be/-Wqq4Wzi7O8 .

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