Question

if A+B+C=180° then prove that cos2A-cos2B+cos2c=1-4sinAcosBsinc​

Answer 1

Answer:

Step-by-step explanation:

A+B+C=180 A+B+C=180

A+B=180-C A+B=180-C

singh(A+B) =sinC cos(A+B) =-cosC

cos2A+cos2B+cos2C

2cos(2A+2B/2) cos(2A-2B/2) +cos2C

2cos(A+B) cos(A-B) +cos2c

2(-cosC) cos(A-B) +2cos²C-1

-1-2cosC(cos(A-B) -cosC)

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

-1-2cosC(2cosAcosB)

-1-4cosAcosBcosC This is your answer