# Help Simplifying Expressions [closed]

I have the following set of equations:

1)

$$\text{b_1} \cos (\text{\beta_1} u)-\text{b_1} \cosh (\text{\beta_1} u)-\text{b2} \cos (\text{\beta_1} \theta y)-\text{d_2} \cosh (\text{\beta_1} \theta y)\sin (\text{\beta_1} u)-\sinh (\text{\beta_1} u)=0$$

2)

$$-\text{b_1} \sin (\text{\beta_1} u)-\text{b_1} \sinh (\text{\beta_1} u)+\text{b_2} \theta \sin (\text{\beta 1} \theta y)-\text{d_2} \theta \sinh (\text{\beta_1} \theta y)+\cos (\text{\beta_1} u)-\cosh (\text{\beta_1} u)=0$$

3)

$$-\text{b_1} \cos (\text{\beta_1} u)-\text{b_1} \cosh (\text{\beta_1} u)+\alpha ^4 \text{b_2} \theta ^2 \cos (\text{\beta_1} \theta y)-\alpha ^4 \text{d_2} \theta ^2 \cosh (\text{\beta_1} \theta y)-\sin (\text{\beta_1} u)-\sinh (\text{\beta_1} u)=0$$

... and I would like to find the constants $$b_1$$, $$b_2$$ and $$d_2$$.

$$b_1 =\frac{\sin \left(\beta _1 u\right)-\sinh \left(\beta _1 u\right)}{\cosh \left(\beta _1 u\right)-\cos \left(\beta _1 u\right)}$$

$$b_2 =\frac{2 \cos \left(\beta _1 u\right) \left(\cos \left(\beta _1 u\right) \cosh \left(\beta _1 u\right)-1\right)}{\theta \left(\cosh \left(\beta _1 u\right)-\cos \left(\beta _1 u\right)\right) \left(\cos \left(\beta _1 \theta y\right) \sinh \left(\beta _1 \theta y\right)+\sin \left(\beta _1 \theta y\right) \cosh \left(\beta _1 \theta y\right)\right)}$$

$$d_2 = -b_2 \frac{\cos \left(\beta _1 \theta y\right)}{\cosh \left(\beta _1 \theta y\right)}$$

... but I want to prove it with Mathematica:

eq={b1 Cos[u β1] - b2 Cos[y β1 θ] -
b1 Cosh[u β1] - d2 Cosh[y β1 θ] +
Sin[u β1] - Sinh[u β1],
Cos[u β1] - Cosh[u β1] - b1 Sin[u β1] +
b2 θ Sin[y β1 θ] - b1 Sinh[u β1] -
d2 θ Sinh[y β1 θ], -b1 Cos[u β1] +
b2 α^4 θ^2 Cos[y β1 θ] -
b1 Cosh[u β1] -
d2 α^4 θ^2 Cosh[y β1 θ] -
Sin[u β1] - Sinh[u β1]}


I want to find the constants {b1, b2, d2}

Solve[# == 0 & /@ eq, {b1, b2, d2}] // Simplify


... The results are large terms and I have trouble simplifying it. Any help would be highly appreciated !

## closed as unclear what you're asking by mikado, MarcoB, Johu, José Antonio Díaz Navas, LCarvalhoOct 26 '18 at 0:40

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• I would verify that the equations and solutions are consistent by substituting numerical values for all variables. – mikado Oct 5 '18 at 22:14
• Since you believe you know the value of b1,b2,d2 then FullSimplify[expr1==0,{b1=..,b2=.., d2=..}] should have pretty good chances of returning True, but it returns b2 Cos[y β1 θ] + (1 + d2 Cosh[y β1 θ]) Sin[u β1] == 0 which tends to make me think there might be a typo or another error. If I try to do the substitutions for b1,b2,d2 the result is even worse. Are you certain no errors slipped through? I tried to carefully undo all your Latex work to get it back into MMA, but I might have made mistakes doing that too. – Bill Oct 6 '18 at 3:55
• Because α does not appear in the solution given, it follows that b2 Cos[y β1 θ] - d2 Cosh[y β1 θ] == 0, which clearly is inconsistent with the solution for d2 in the question. I believe that there are errors in eq. – bbgodfrey Oct 6 '18 at 4:18
• @Bill Thank you very much for your comment and your help ! Indeed this might be a mistake on my side. I will check everything again... but this might take a while. – james Oct 6 '18 at 7:15
• @bbgodfrey Thanks for your comment. Yes, there is an error somewhere. As I have already told Bill, I will check everything again. However, this might take a while... – james Oct 6 '18 at 7:16