How do you determine when an equation involving trigonometric terms can be solved analytically? For example I have something like sin(x) + cos(y) + a + x = 0 and am asked if that can be solved analytically.I Have tried manipulating the equation, but that doesn't seem very good to prove that it can't be solved analytically.
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What sort of methods are used to determine if something can be solved analytically, besides "I tried for a while and couldn't solve it analytically, therefore it's not solveable analytically" which isn't a valid argument... I think there must be some area of maths which provides rules to classify these functions. Does anyone know what that area of maths is called? Or some rules which apply in this case?