I came across this question while doing trigonometry. I have tried everything that I could possibly think of, AM/GM, converting it into quadratic equation, conditional identities, solving from RHS, solving from LHS, however, have not gotten anywhere. Please help me!
Question: In triangle ABC, prove that: $$(\sin A + \sin B)(\sin B+\sin C)(\sin C+\sin A) \gt \sin A \sin B \sin C$$
$\sin A+\sin B>\sin A,\sin B+\sin C>\sin B,\sin C+\sin A>\sin C$. Take product.