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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.

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.

Grade:12

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
9 years ago
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

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