Prove that sinh(x+y)=sinxcoshy+coshxsinhy

Maiclubk 2021-02-27 Answered
Prove that sinh(x+y)=sinxcoshy+coshxsinhy
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Expert Answer

krolaniaN
Answered 2021-02-28 Author has 86 answers

sinh(A)=eˣeˣ2 by definition when A=x, so, if A=x+y:
sinh(x+y)=ex+y(e(x+y))2.
cosh(x)=eˣ+eˣ2 by definition.
sinh(x)cosh(y)=(exex)ey+ey4=ex+y+exyeyxe(x+y)4.
cosh(x)sinh(y)=(ex+ex)eyey4=ex+yexy+eyxe(x+y)4.
When we add these last two equations we get sinh(x)cosh(y)+cosh(x)sinh(y)=
2ex+ye(x+y)4=ex+ye(x+y)2=sinh(x+y)

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P(t) models the distance of a swinging pendulum (In CM) from the place it has travelled t seconds after it starts to swing. Here, t is entered in radians.
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