cos(12 degress)*cos(24 degrees)*cos(48 degrees)*cos(96 degrees)

I thought to use MuPAD 4.0 to calculate the exact value of

cos(12 degress)*cos(24 degrees)*cos(48 degrees)*cos(96 degrees)

i.e. cos(PI/15)*cos(2*PI/15)*cos(4*PI/15)*cos(8*PI/15)

I used...

rewrite(cos(PI/15)*cos(2*PI/15)*cos(4*PI/15)*cos(8*PI/15),exp)
expand(%)
simplify(%)

and other combinations along those lines, but could not get MuPAD to do the
calculation.

I decided to do it by hand and multiplied out the exponential terms to
obtain...

(-1 + sum 15th roots of -1)/16

i.e. (-1 + 0)/16 = -1/16


Is there a set of commands to do this expansion in exponentials and
simplification in MuPAD to get -1/16?

Do other CAS's do this nicely?

Interestingly, when I asked MuPAD to float the original expression it came
up with -0.0625 which is -1/16 and exactly correct. I wonder how MuPAD did
that so exactly. I suspect there is a different way to attack the question.

Cheers,
Brad


.

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