The Minimum value of `27^cosx +81^sinx` is equal toA. `(2)/(3sqrt3)`B. – InterviewSolution

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1.	The Minimum value of `27^cosx +81^sinx` is equal toA. `(2)/(3sqrt3)`B. `(2)/(9sqrt3)`C. `(4)/(3sqrt3)`D. none of these
Answer» Correct Answer - B We known that `A.M. ge G.M.` `therefore(27^(cosx)x+81^(sinx))/(2)gesqrt(27^(cosx)xx81^(sinx))` `implies27^(cosx)+81^(sinx)ge2sqrt(3^(3cosx+4sinx))` `implies27^(cosx) +81^(sinx)ge2xxsqrt(3^(-5))` `" "[because-5le3cosx+4sinxle5]` `implies27^(cosx)+81^(sinx)ge(2)/(9sqrt3)` Hence, the minimum value of `27^(cosx)+81^(sinx)is(2)/(9sqrt3).`

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