Practicing Success
The value of the expression cos 24° + cos 55° + cos 125° + cos 204° + cos 300°: |
\(\frac{1}{2}\) -\(\frac{1}{2}\) 1 2 |
\(\frac{1}{2}\) |
cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = ( cos 24° + cos 204° ) + ( cos 55° + cos 125° ) + ( cos 300° ) = [ cos 24° + cos (180° + 24°)] + [ cos 55° + cos (180° - 55°)] + [ cos (360° - 60°)] = [ cos 24° - cos 24° ] + [ cos 55° - cos 55° ] + cos 60° {because cos ( 180 + θ ) = - cos θ, cos ( 180 - θ ) = - cos θ, cos (360 - θ) = cos θ} = cos 60° = \(\frac{1}{2}\) |