Q9 of 51 Page 54

Prove: cos x + cos(120 – x) + cos(120 + x) = 0

FORMULA: -


(i)


Proof:



⇒ cosx + cos (120 – x) + cos (120 + x) = cosx + 2cos120 cos( – x)


⇒ cosx + cos (120 – x) + cos (120 + x) = cosx + 2cos(180 – 60) cosx


⇒ cosx + cos (120 – x) + cos (120 + x) = cosx + 2 ( – cos 60) cosx



⇒ cosx + cos (120 – x) + cos (120 + x) = cosx – cosx


⇒ cosx + cos (120 – x) + cos (120 + x) = 0


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