Hello List

I tried Sage for simplifying some trigonometric expressions.

sage: a=cos(pi/11)+cos(3*pi/11)+cos(5*pi/11)+cos(7*pi/11)+cos(9*pi/11)
sage: a.simplify_trig()
cos(pi/11)+cos(3*pi/11)+cos(5*pi/11)+cos(7*pi/11)+cos(9*pi/11)

This sum is equal to 1/2 then I try:

sage: a=cos(pi/11)+cos(3*pi/11)+cos(5*pi/11)+cos(7*pi/11)+cos(9*pi/
11)-1/2
sage: a.simplify_trig()
cos(pi/11)+cos(3*pi/11)+cos(5*pi/11)+cos(7*pi/11)+cos(9*pi/11)-1/2

I try with simplify_full() too, no more result.

Another example:
sage: b=atan(2)+atan(5)+atan(8)
sage: b.simplify_full()
atan(2)+atan(5)+atan(8)

This sum is equal to 5*pi/4
The only thing  I succed to do is:

sage: b=atan(2)+atan(5)+atan(8)
sage: simplify_trig(tan(b))
1

If you have any idea to give those results, thanks in advance

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