The value of the expression cos 25° + cos 40° + cos 140° + cos 205° + cos 300°:
Answer & explanation
Correct answer: option 2
cos 25° + cos 40° + cos 140° + cos 205° + cos 300°
= ( cos 25° + cos 205° ) + ( cos 40° + cos 140° ) + ( cos 300° )
= [ cos 25° + cos (180° + 25°)] + [ cos 40° + cos (180° - 40°)] + [ cos (360° - 60°)]
= [ cos 25° - cos 25° ] + [ cos 40° - cos 40° ] + cos 60°
{because cos ( 180 + θ ) = - cos θ, cos ( 180 - θ ) = - cos θ, cos (360 - θ) = cos θ}
= 0 + 0 + cos 60°
= \(\frac{1}{2}\)