cos²a+cos²b-cos²c=1-2sina.sinb.sinc
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Answer:
2cosAcosBcosC =(2cosAcosB)cosC
=(cos(A+B) + cos(A-B))cosC
=cos(pi-C)cosC + cos(A-B)cos(pi-(A+B))
=-2cos^2C - 2cos(A+B)cos(A-B)
=-cos^2C - cos^2A + sin^2B
so,
1 - 2cosAcosBcosC = 1 + cos^2C + cos^2A - sin^2B
= 1 - sin^2B + cos^2C + cos^2A
= cos^2B + cos^2C + cos^2A
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