Question

Please guys answer this question . If A,B,c are angles of a traingle then what is the value of sin A-sin B +sinc here we can take A+B+C =180 degree​

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

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