Prove that cos 20 degree-cos 40 degree-cos 80 degree is equal to zero
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To prove
cos80+cos40−cos20=0
Apply the following
cosA+cosB=2cos(A+B2)cos(A−B2)
cos60=12
Therefore,
cos80+cos40=2cos(80+402)cos(80−402)
=2cos60cos20
=2⋅12cos20
=cos20
So,
cos80+cos40−cos20=cos20−cos20=0
QED
cos80+cos40−cos20=0
Apply the following
cosA+cosB=2cos(A+B2)cos(A−B2)
cos60=12
Therefore,
cos80+cos40=2cos(80+402)cos(80−402)
=2cos60cos20
=2⋅12cos20
=cos20
So,
cos80+cos40−cos20=cos20−cos20=0
QED
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