PROVE THAT

MaxWong:

The "659" error is a rounding off error in your calculator. I just verified it to 1000 decimal places and still holds true. It is EXACTLY 1/8.

It's NOT equal to 1/8 ........It equals to 0.1250000000000659. Notice the 659 at the last

I happen to remember this from trig class....

Note that we can write

sin 40  = 2sin20cos 20    rearrange

cos20  = sin40/ [2 sin20]

And....likewise

sin80 = 2sin40cos40

cos40 = sin80 /[2sin40]

And

sin160 = 2sin80cos80

cos80 = sin160/[2sin80]

So

cos20*cos40*cos80  =

sin40/ [ 2sin20]  * sin80/ [2sin40]   *  sin160 / [2sin80] =

sin160 / [8 sin20] =

(1/8) sin160/sin20

Note that sin160  =   sin(180 - 20)   =  sin180cos20 - sin20cos180  =  sin20

So

(1/8)sin20 / sin20   =

(1/8)