Take L.H.S:

cos 20° cos 100° + cos 100° cos 140° - cos 140° cos 200°

Multiplying & Dividing by 2:

{∵ 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