Question

Prove that cos 20 degree-cos 40 degree-cos 80 degree is equal to zero

Answer 1

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