The value of the expression cos 24° + cos 55° + cos 125° + cos 204° + cos 300°:
Answer & explanation
Correct answer: option 1
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°
= \(\frac{1}{2}\)