Question

If A+B+C =180°, then cos(A+B) =
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Answer 1

Answer:

cos2A + cos2B – cos2C = cos2A – sin2B + cos2C + 1 = cos(A + B) cos(A – B) + cos2C + 1 = cos(180° – C) cos(A – B) + cos2C + 1 = –cosC cos(A – B) + cos2C + 1 = 1 – cosC [cos(A – B) – cosC] = 1 – cosC [cos(A – B) – cos(180° – (A + B))] = 1 – cosC [cos(A – B) + cos(A + B)] = 1 – cosC [2 cosA cosB] = 1 – 2 cosA cosB cosCRead more on Sarthaks.com - https://www.sarthaks.com/490241/if-a-b-c-180-then-show-that-cos-2a-cos-2b-cos-2c-1-2-cosa-cosb-cosc

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