Why is running this code always displaying Running?

Clear["Global*"]
Maximize[{Tan[a], a + b + c == \[Pi],
Sin[a] + 3 Sin[b] Cos[c] == 0, \[Pi]/2 < c < \[Pi],
0 < a < \[Pi]/2, 0 < b < \[Pi]/2}, {a, b, c}] // FullSimplify


Why is running this code always displaying Running? No calculation results

We calculate the max value of a, then Tan[a] since Tan is increasing in 0 < a < π/2

max=Maximize[{a, a + b + c == π,
Sin[a] + 3 Sin[b] Cos[c] == 0, π/2 < c < π, 0 < a < π/2,
0 < b < π/2}, {a, b, c}]
Tan[max // First] // FullSimplify


3/4

• That is to say, if the maximum value of the function cannot be obtained in one step, then use monotonicity to find the maximum value of the independent variable first May 29, 2023 at 0:32

Or use a numeric method

\$Version

(* "13.2.1 for Mac OS X ARM (64-bit) (January 27, 2023)" *)

Clear["Global*"]

{max, arg} =
NMaximize[{Tan[a], a + b + c == π,
Sin[a] + 3 Sin[b] Cos[c] == 0, π/2 < c < π,
0 < a < π/2, 0 < b < π/2}, {a, b, c},
WorkingPrecision -> 30] // N // Rationalize

(* {3/4, {a -> 0.643501, b -> 0.463648, c -> 2.03444}} *)