In 12.2.0 for Microsoft Windows (64-bit) (December 12, 2020), once defined:

eqn1 = {Cos[t] == 0, 0 < t < Pi};
eqn2 = {TrigToExp[Cos[t]] == 0, 0 < t < Pi};

solving the respective equations:

sol1 = NSolve[eqn1, WorkingPrecision -> 5]
sol2 = NSolve[eqn2, WorkingPrecision -> 5]

we get:

{{t -> 1.5708}}


therefore, through the checks:

Cos[t] == TrigToExp[Cos[t]] // Simplify
eqn1 /. sol1
eqn2 /. sol1

we get:


{{True, True}}

{{True, True}}

Am I missing something or is something wrong in NSolve?


I am not sure why you had to use WorkingPrecision -> 5 for.

But due to your use of TrigToExp, NSolve will now do it if you add the domain Complexes


Mathematica graphics

Help on NSolve says

assumes by default that quantities appearing algebraically in inequalities are real

Compare to

 (*  {} *}
  • $\begingroup$ I was missing this detail, thanks! WorkingPrecision I used it to get True everywhere in checks. Thanks again! $\endgroup$ – TeM May 12 at 9:35

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