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As proved by @Juanjo , the correct response can be obtained by transforming the original form of f(x) in f(x).trig_reduce().trig_simplify().trig_reduce(). This is now Trac#34757

A different but similar problem with Maxima has been identified and reported.

The fact that algorithm="sympy"never returns has been explored, shown to be a genuine Sympy problem and reported.

HTH,

As proved by @Juanjo , the correct response can be obtained by transforming the original form of f(x) in f(x).trig_reduce().trig_simplify().trig_reduce(). This is now Trac#34757

A different but similar problem with Maxima has been identified and reported.

The fact that algorithm="sympy"never returns has been explored, shown to be a genuine Sympy problem and reported.

HTH,

EDIT : The problem of numerical computation is reformulated here.