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CGP EDU Academic Team
Published on: August 12, 2026
If A + B + C = π then prove that cos2A + cos2B – cos2C = 1 – 4 sinA sinB cosC
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Sol. L.H.S cos2A + cos2B – cos2C
= 2 cos (A + B) cos (A –B) – cos2C
= 2 cos ( π – C) cos (A –B) – cos2C
= – 2 cosC cos (A – B) – 2cos 2 C +1
= – 2 cosC [cos (A – B) + cosC ]+1
= – 2 cosC [cos (A – B) – cos (A + B) ]+1
= –2cosC [2sin A sin B]+1
= 1 – 4 sinA sinB cosC
= R.H.S
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