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

Brad Cooper wrote:
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?
[snip]

With Mathematica 5.2:

FullSimplify[Cos[Pi/15]*Cos[2*(Pi/15)]*Cos[4*(Pi/15)]*Cos[8*(Pi/15)]]

-(1/16)

Regards,
Jean-Marc
.

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