Question

If A+B+C = 180°,Prove that
Cos 2A + Cos 2B + Cos2C = -1-4 CosA CosB CosC​

Answer 1

Answer:

2 cos(A+B) cos(A-B) +2cos^2 C-1

2[-cosC]cos(A-B)+2cos^2C - 1

-1-2 cosC[cos(A-B) - CosC]

-1-2[cos(A-B)+cos(A+B)]cosC

-1-2[2cosAcosB]cosC

-1-4cosAcosBcosC