Question

maximam and minimam value SinAsinBSinC

Answer 1

sinx is concave in (0,π), therefore,sinA+sinB+sinC3≤sin(A+B+C3)(1)Since, A, B, C are angles of a triangle, (1) gives,sinA+sinB+sinC≤33–√2(2)Since the upper bound in (2) can be easily achieved by setting A=B=C, the upper bound is tight. Hence the required maximum is 33√2.