Hyperbolic Trigonometric Identity: cosh(x+y)

in Threespeak2 months ago

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In this video I go prove the hyperbolic trigonometric identity cosh(x+y) = cosh x cosh y + sinh x + sinh y. I had proved same identity several years back in my earlier video, but that proof simply involved back-calculating that the identity was correct. In this video though, I show how to go about proving the identity without knowing the final result. I show this by illustrating that the cosh(x + y) involves a multiplication of exponents, which can also result by multiplying cosh and sinh functions together in several variations. Thus I show how to reverse a foil expansion process and ultimately obtain cosh(x+y) in terms of cosh x, cosh y, sinh x, and sinh y. This is a very interesting proof video in that I show that we need to think ahead at what we ultimately want before we begin attempting to derive an identity; so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvtVnszc8jhu0oC3-Q

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

Related Videos:

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 .


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