Question

Show that_ cos A +cos(120°+A) + cos(120°-A)=0​

Answer 1

|| ✰✰ ANSWER ✰✰ ||

Use the addition formula for cosine

cos(alpha + beta) = cos(alpha) × cos(beta) - sin(alpha) × sin(beta)

(see the lesson Addition and subtraction formulas in this site)

You will have

cos(120+A) = cos(120) × cos(A) - sin(120) × sin(A),

cos(120-A) = cos(120) × cos(A) + sin(120) × sin(A).

Add these two equality (both sides).

You will get

cos(120+A) + cos(120-A) = 2cos(120) × cos(A).

Now use that cos(120) = -1 / 2

Hence 2cos(120) = -1.

Hence,

cos(A) + cos(120+A) + cos(120-A) = cos(A) + 2cos(120)*cos(A) = cos(A) - cos(A) = 0

✪✪ Hence Proved ✪✪

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Answer 2

Hope it helps you!!

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