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October 21st, 2016, 04:38 AM   #1
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solve hyperbolic equation

Find all real solutions of

4sinh4x - 17sinh3x + 4sinh2x = 0

This is a worked example in my text book. The working says it's possible to combine two of the hyerbolic sines together using an identity to get

4(2sinh3x.coshx) - 17sinh3x = 0

So sinh4x + sinh2x = 2sinh3x.coshx

I can't see how to do this, the book doesn't show the steps. Can anyone show me how it's done and/or which identity to use?

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October 21st, 2016, 05:43 AM   #2
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Below are various standard identities for the hyperbolic functions. The first one will help you (by using A = 4x and B = 2x). There are many more (not just ones listed below), corresponding to the various trigonometric function identities.

sinh(A) + sinh(B) ≡ 2sinh((A + B)/2)cosh((A - B)/2)
cosh(A) + cosh(B) ≡ 2cosh((A + B)/2)cosh((A - B)/2)
sinh (A + B) ≡ sinh(A)cosh(B) + cosh(A)sinh(B)
sinh (A - B) ≡ sinh(A)cosh(B) - cosh(A)sinh(B)
cosh (A + B) ≡ cosh(A)cosh(B) + sinh(A)sinh(B)
cosh (A - B) ≡ cosh(A)cosh(B) - sinh(A)sinh(B)
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