cos(20°) + cos(60°) + cos(100°) + cos(140°) =
1/2
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Step-by-step explanation:
cosA+cosB= 2cos((A+B)/2)cos((A-B)/2)
cos(180-A)= -cosA [A=any angel]
cos20+cos100
= 2cos((20+100)/2)cos((100-20)/2)
=2cos60 cos40 [cos60=1/2]
=cos40
cos20+cos60+cos100+cos140
=cos40+cos60+cos140
=cos40+1/2+cos(180-40)
=cos40+1/2-cos40
=1/2 [proved]
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