prove that cos20°cos30°cos40°cos80°=√3/16
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Step-by-step explanation:
Cos20.co30.cos40.cos80=root3/16
LHS=1/2 {2cos20.cos40} cos30.cos80
=1/2 {cos60+cos20} cos30.cos80
=1/4cos30.cos80+1/2cos30.co20.cos80
=root3/8.cos80 +root3/8 {2cos20.cos80}
=root3/8.cos80+ root3/8 (cos100+cos60)
=root3/8cos80 +root3/8ccos (180-80)+root3/8cos60
=root3/16=RHS.
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