In this video I go over the derivation for the hyperbolic trig identity sinh(x + y) = sinh(x)cosh(y) + cosh(x)sinh(y). This derivation is very similar to the one I did for cosh(x + y) in that I show how we need to think of the final result we want before we start the derivation. In other words we need to use the definition of cosh and sinh by multiplying them together to obtain sinh(x+y). Note though that in my earlier video several years back I derived this same identity but by simply working backwards proving the given identity. But in this video I work from start to finish to show how we sometimes have to think outside of the box instead of the typical linear thinking derivations; so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvwZUa6EG1pWW-hq7Q
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-hyperbolic-trigonometric-identity-sinh-x-y
Related Videos:
Hyperbolic Trigonometric Identity: cosh(x-y):
Hyperbolic Trigonometric Identity: cosh(x+y):
Hyperbolic Functions - tanh(x), sinh(x), cosh(x) - Introduction:
Hyperbolic Trigonometry Identity Proof: sinh(x+y) = sinh(x)cosh(y) + cosh(x)sinh(y):
Hyperbolic Trigonometry Identity Proof: sinh(-x) = -sinh(x), cosh(-x) = cosh(x): .
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STOPI don't always derive the hyperbolic trig identity for sinh(x+y) but when I do I usually follow the same method as for cosh(x+y) ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-hyperbolic-trigonometric-identity-sinh-x-y