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Answer to Question #13524 in Trigonometry for sunil

Question #13524
cos20*cos40*cos60*cos80
Expert's answer
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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