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October 21st, 2016, 04:38 AM  #1 
Member Joined: Mar 2015 From: uk Posts: 33 Thanks: 1  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? Thanks 
October 21st, 2016, 05:43 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,375 Thanks: 2010 
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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