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Prove that :

cos 20° cos 100° + cos 100° cos 140° - cos 140° cos 200° = -(3/4)

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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

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