Prove that, cos24° + cos55° +cos125° + cos204°+ cos300°=$\frac{1}{2}$
Solution:
L.H.S:
cos24° + cos55° +cos125° + cos204°+ cos300°
= cos24° + cos55° +cos125° + cos(180°+24°)+ cos(360°-60°)
= cos24° + cos55° + cos125°-cos24°+cos60°
= cos55+cos(180°-55°) + $\frac{1}{2}$
= cos 55° –cos55° + $\frac{1}{2}$
= $\frac{1}{2}$
= R.H.S [Proved]