Question

if cos(B-C)+cos(C-A)+cos(A-B)=-3/2 then prove that cosA+cosB+cosC=O and sinA+sinB+sinC=O after that prove that cos(B-C)=cos(C-A)=cos(A-B)=-1/2

Answer 1

google is your friend. You might start here:

https://math.stackexchange.com/questions/2132148/if-cosa-bcosb-ccosc-a-frac-32-prove-that-cosacosbcosc-sinas