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As it turns out, we already have it, just not with all possible aliases! I didn't even know this.

sage: m = matrix([[sin(x), cos(x)], [sin(x), cos(x)]]); m
[sin(x) cos(x)]
[sin(x) cos(x)]
sage: o = m*m.transpose()
sage: o.simplify_trig()
[1 1]
[1 1]

But the ticket referenced in the comment above should make all of them available.