Question

PROVE THAT:-

cos20* x cos40* x cos60* x cos80*= 1/16

Answer 1

Step-by-step explanation:

=cos20°×cos40°×cos80°×1/2

={cos20°×cos40°}×cos80°×1/2

=1/2{2cos20°×cos40°}×cos80°×1/2

=1/4{cos(20°+40°)+cos(20-40)°}×cos80°

=1/4cos60°cos80°+1/4cos20°cos80°

=1/8cos80°+1/8{2cos20°×cos80°}

=1/8cos80°+1/8{cos100°+cos60°}

=1/8cos80°+1/8cos100°+1/8cos60°

=1/8cos(180-100)°+1/8cos100°+1/16

= -1/8cos100°+1/8cos100°+1/16

=1/16.

Hence proved.

Answer 2

Answer:

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