Output of Reduce + Simplify

I'm using Reduce to solve some equations and then simplify to eliminate some undesired results. The problem is that, when I apply Simplify, it messes with my output from reduce. As an example:

eq = Cos[x] + Sin[x] == y
Reduce[eq, x]
Simplify[Reduce[eq, x]]

My outputs are

(C \[Element] Integers && y == -1 && (x == -(\[Pi]/2) + 2 \[Pi] C || x == \[Pi] + 2 \[Pi] C)) || (C \[Element] Integers && 1 + y != 0 && (x == 2 ArcTan[(1 - Sqrt[2 - y^2])/(1 + y)] + 2 \[Pi] C ||x == 2 ArcTan[(1 + Sqrt[2 - y^2])/(1 + y)] + 2 \[Pi] C))

And with Simplify:

(C \[Element] Integers && y == -1 && (\[Pi] + 2 x == 4 \[Pi] C || \[Pi] + 2 \[Pi] C ==x)) || (C \[Element] Integers && 1 + y != 0 && (x == 2 (ArcTan[(1 - Sqrt[2 - y^2])/(1 + y)] + \[Pi] C) || x == 2 (ArcTan[(1 + Sqrt[2 - y^2])/(1 + y)] + \[Pi] C)))

Of course, Simplify here is not necessary, but my real equations are rather long to put here. My point is, when I use simplify, I get x to the lhs, so I can't use ToRules to make a list of rules from my output. I sounds like a silly question, but I've tried a lot of different things and I cant figure it out how to do it...

Thank you so much

• I can make it work for some cases: ToRules[x - a == b + c + d] /. ((x + lhs_) -> rhs_) :> (x -> (-lhs + rhs)) will produce the desired result, but if my lhs is (-x+a) it won't work... – Fábio Sep 5 at 1:22
• Sometimes you get x==complicated and you would like x==simple but Simplify thinks the result is simpler if it pushes things across the ==. For those cases try x==complicated/.Equal[left_,right_]:>Equal[Simplify[left],Simplify[right]]` For x+complicated==morecomplicated try x+complicated==morecomplicated /.Equal[left_,right_]:>Solve[Equal[left,right],x] or even replace that Solve with Reduce and see if that works for you. If you can show more specific examples that still don't work then perhaps someone can show a general method that works for you. – Bill Sep 5 at 4:43
• Well, it's working so far. I'll try to come with a more general method if someone comes with the same issue. Thank you! – Fábio Sep 6 at 19:43