Show that cos°20 cos°40 cos°60 cos°80 =1/16
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Step-by-step explanation:
cos20cos40cos60cos80
=1/2cos20(cos40cos80)
=1/4cos20(2cos40cos80)
=1/4cos20[cos(40+80)+cos(40-80)]
=1/4cos20[cos120+cos40]
=1/4cos20[cos(180-60)+cos40]
=1/4cos20[-1/2+cos40]
=-1/8cos20+1/4cos40cos20
=-1/8cos20+1/8(2cos40cos20)
=-1/8cos20+1/8[cos60+cos20]
=-1/8cos20+1/8[1/2+cos20]
=-1/8cos20+1/16+1/8cos20
=1/16
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