Hyperbolic Trigonometric Identity: sinh(x-y)

in Threespeak2 months ago (edited)

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In this video I go over a quick derivation of the hyperbolic trig identity sinh(x – y) = sinh(x)cosh(y) – cosh(x)sinh(y). The derivation simply uses my past work on the proof for sinh(x + y) = sinh(x)cosh(y)+cosh(x)sinh(y) and simply replaces y with -y. Thus using the definitions of sinh and cosh I show that cosh(-y) = cosh(y) and sinh(-y) = - sinh(y). Thus the only that changes when compared to the sinh(x+y) identity is we subtract instead of add the two terms together. This is a simple and quick derivation but shows the importance of building up previous work, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvwoBncxK428IJFN0Q

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/3xyhuv-video-notes-hyperbolic-trigonometric-identity-sinh-x-y

Related Videos:

Hyperbolic Trigonometric Identity: sinh(x+y): https://youtu.be/CtBzwqd4Rqc
Hyperbolic Trigonometric Identity: cosh(x-y): https://youtu.be/GMGaQTym4d4
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) = -sinh(x), cosh(-x) = cosh(x): http://youtu.be/-Wqq4Wzi7O8 .


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