# Simplify doesn't simplify multiple conditions from Reduce

Consider the following simple example where I try to solve an equation and then apply a bounded interval to find the right result out of an infinite amount of solutions:

Eq4 = -1 == (Cos[δ] Sin[t])/(Cos[φ ] Sin[δ] - Cos[t] Cos[δ] Sin[φ])
tS = Simplify[(Reduce[Eq4, {t}] /. {δ -> -0.401426, φ -> 0.841248699}) && (0 < t < π/2)]

(* Out:
C[1] ∈ Integers && (t == -2.72982 + 2 π C[1] || t == 0.869424 + 2 π C[1]) && 0 < t < π/2
*)


Why isn't the last one just simplified to t == 0.869424 and how can I achieve it?

• First@Solve[0 <= t <= \[Pi]/2 && Reduce[Eq4, {t}] /. {\[Delta] -> -0.401426, \[CurlyPhi] -> 0.841248699}, {t, C[1]}] Commented Jan 28, 2016 at 0:34
• You can simply include the domain restriction in your system of equations instead. A simple Reduce[{Eq4, 0 < t < Pi/2} /. {δ -> -0.401426, φ -> 0.841248699}, t] readily returns t == 0.869424. Commented Jan 28, 2016 at 1:38
• @MarcoB and march: Both of your solutions work. However in both cases I get the warning "Solve/Reduce was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result.". It would be nice, but not necessary to get rid of it. If you post your comments as answers I'll accept (one of) them. Commented Jan 28, 2016 at 13:02
• @march see above comment. Commented Jan 28, 2016 at 13:02

You can simply include the domain restriction in your system of equations instead:

Eq4 = -1 == (Cos[δ] Sin[t])/(Cos[φ ] Sin[δ] - Cos[t] Cos[δ] Sin[φ])
Reduce[{Eq4, 0 < t < Pi/2} /. {δ -> -0.401426, φ -> 0.841248699}, t]
(* Out: t == 0.869424 *)


Reduce complains that it "was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result". That really does not influence the result you get in this case, but if it bothers you, you could

1) provide exact values for δ and φ;

2) Rationalize the numerical ones you have as follows:

Reduce[{Eq4, 0 < t < Pi/2} /. Rationalize[{δ -> -0.401426, φ -> 0.841248699}, 0], t] // N
(* Out: t == 0.869424 *)


3) simply suppress the printing of the message using Quiet:

Quiet@Reduce[{Eq4, 0 < t < Pi/2} /. {δ -> -0.401426, φ -> 0.841248699}, t]