Question: A bug in applyrule?

This looks like a bug to me but please correct me if it is not.

restart;

kernelopts(version);

`Maple 2021.2, X86 64 LINUX, Nov 23 2021, Build ID 1576349`

half_angle_rule := [
        sin(x::name) = 2*sin(x/2)*cos(x/2),
        cos(x::name) = 1 - 2*sin(x/2)^2
];

[sin(x::name) = 2*sin((1/2)*x)*cos((1/2)*x), cos(x::name) = 1-2*sin((1/2)*x)^2]

In this example, Maple applies the rule to the first element only.
It should apply to both.

A := < sin(u), sin(u) >;
applyrule~(half_angle_rule, A);

Vector(2, {(1) = sin(u), (2) = sin(u)})

Vector[column](%id = 36893628627946684772)

In this example, Maple applies the rule to the second element only.
It should apply to both.

B := < cos(u), cos(u) >;
applyrule~(half_angle_rule, B);

Vector(2, {(1) = cos(u), (2) = cos(u)})

Vector[column](%id = 36893628627946688132)

Download applyrule-bug1.mw

 

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