InterviewSolution
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InterviewSolution
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Statement-1 : If angles A, B, C of `DeltaABC` are acute, then `cotA cotB cotCle(1)/(3sqrt(3)).` Statement-2: If a, b, c are positive real numbers and `-ltmlt1`, then `(a^(m)+b^(m)+c^(m))/(3)lt((a+b+c)/(3))^(m)`A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - B Using `A.M.geG.M.,` we have `(tanA+tanB+tanC)/(3)ge(tanAtanBtanC)^(1//3)` `implies" "(tanAtanBtanC)/(3)ge(tanAtanBtanC)^(1//3)` `" "[becausetanA+tanB+tanC=tanAtanBtanC]` `implies" "(tanAtanBtanC )^(2//3)ge3` `implies" "tanAtanBtanCge3sqrt(3)impliescotAcotBcotCle(1)/(3sqrt(3))` Hence, statement-1 is true. Statement-2 is also true but it is not a correct explanation for statement-1. |
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