cos 20° cos 100° + cos 100° cos 140° - cos 140° cos 200° = -(3/4)
Take L.H.S :
cos 20° cos 100° + cos 100° cos 140° - cos 140° cos 200°
Multiplying & Dividing by 2 :
= \(\frac{1}{2}\){cos 100° cos 20° + 2 cos 140° cos 100° - 2 cos 200° cos 140°}
{∵ 2 cos A cos B = cos (A + B) + cos (A – B)}
{cos (180° + A) = - cos A ;
cos (90° + A) = - sin A &
cos (360° - A) = cos A}
= R.H.S.
Hence Proved