Question #67c01

1 Answer
Cri007 · Douglas K.
Jun 4, 2017

See below.

Explanation:

Set

#cos20cos40cos60cos80=a#

multiply both sides by #sin20#.

#sin20cos20cos40cos60cos80=asin20#

By double angle formula,

#sin20cos20=1/2sin40#

We can continue this pattern.

#1/2sin40cos40cos60cos80=asin20#

#1/4sin80cos80cos60=asin20#

#1/8sin160cos60=asin20#

#cos60# is simply #1/2#

So,

#1/16sin160=asin20#

However,

#sin160=sin20#

So, #a=1/16#, and we have proven the statement.

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