Question

Prove that cos A + cos (120° – A) + cos(120° + A) = 0

Answer 1

L.H.S. = cosA + cos A(120° – A) + cos(120° + A) 

= cosA + 2cos 120°. cosA 

= cosA + 2cosA (-cos60°) {∵ cos 120° = cos (180° - 60°) = -cos 60°}

= cos A – 2 cosA . \(\frac{1}{2}\) = 0 = R.H.S.

Comments

3rd line how

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{∵ cos 120° = cos (180° - 60°) = -cos 60°}