Question

coa2A + cos2B+cos2C=-1-4cosAcosBcosC​

Answer 1

Step-by-step explanation:

Given: A+B+C=π

L.H.S=cos2A+cos2B+cos2C

=[2cos(A+B)cos(A−B)]+(2cos

2

C−1)........cosC+cosD=2cos

2

C+D

cos

2

C−D

=2cos(180−C)cos(A−B)+2cos

2

C−1

=−2cosC(cos(A−B)−cosC)−1

=−2cosC(cos(A−B)+cos(A+B))−1

=−2cosC(2cosAcosB)−1

=−4cosAcosBcosC−1