Answer to Question #13549 in Trigonometry for Basu
Show that cos20°cos40°cos60°cos80°=1/16
1
2012-08-23T08:32:29-0400
cos20*cos40*cos60*cos80=
At first multiply the expression by sin20 and divide by sin20:
= sin20.cos20.cos40.cos60.cos80/sin20
Since sin20*cos20=1/2 (sin 0+sin40) we obtain
=sin40*cos40*cos60*cos80/{2 sin20}
Also sin40*cos40=1/2 sin80
so we get
=sin80*cos80*cos60/{4 sin20}
Again sin80*cos80=1/2 sin160
and finally
=sin160*cos60/{8sin20}=1/16
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