If A+B+C=180 degrees, prove that :-

If A, B, C be the angles of a triangle ABC then (sinA+sinB)(sinB+sinC)(sinC+sinA)>sinAsinBsinC.

Hello student,

By the concept of AM >= GM
(sinA+sinB)/2 >root(sinAsinB)
(sinB+sinC)/2>root(sinBsinC)
)(sinC+sinA)/2>root(sinAsinC)

Multiplying all three equations we will get the required..
Hence proved