Solving for 2 Unknowns with 3 Equations and Sine Functions

[boeledi]

Could someone help me find the solution of this ?

x - y + z - 2 A sin(y+z) = C
-x - y - z - 2 A sin(x+z) = C
-x + y + z - 2 A sin(x+y) = C

Where C and A are constant ?
Many thanks

 

[Gokul43201]

could you please confirm that the second line is not x + y - z ...

 

[boeledi]

Sorry, based on your question, I did my calculations again and ... The real system is:

-x + y + z + 2A sin(y-z) = C
-x + y - z + 2A sin(x-z) = C
x + y - z + 2A sin(x-y) = C

where A and C are constant.

Could you please help me?

 

[Integral]

I would start by applying the trigonometric identities for sin(a+b) then add the first 2 equations together. I think several terms will drop out, you then should be able to repeat the process with the 3rd equation. The goal is to eliminate one of the variables, when you have an expression involving 2 variables solve for 1 of them, then use that to back substitute isolating the remaining variables.

 

[Mark]

5 unkowns
2 of which are constant
3 equations

combine 3 equations, you will be left with 2 unkowns (your two constants)

And you are done... all you need is the time to solve it.