Question

Ifa+b+c=pi then prove that cos square a/2+cos square b/2-cos square c/2=2cos a/2 cos b/2 sinc/2

Answer 1

Answer:

Given: A+B+C=π

L.H.S=cos2A+cos2B+cos2C

=[2cos(A+B)cos(A−B)]+(2cos2C−1)........cosC+cosD=2cos2C+Dcos2C−D

=2cos(180−C)cos(A−B)+2cos2C−1

=−2cosC(cos(A−B)−cosC)−1

=−2cosC(cos(A−B)+cos(A+B))−1

=−2cosC(2cosAcosB)−1

=−4cosAcosBcosC−1