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If a in (0,1)a n df(a)=(a^2-a+1)+(8sin^2...

If `a in (0,1)a n df(a)=(a^2-a+1)+(8sin^2a)/(sqrt(a^2-a+1))+(27 cos e c^2a)/(sqrt(a^2-a+1))` , then the least value of `(f(a))/2` is_______

Text Solution

Verified by Experts

The correct Answer is:
18
Using `A.M.ge G.M.` (forpositive numbers)
`(s^2-a+1)+(8sin^2a)/sqrt(a^2-a+1)+(27cosec^2a)/sqrt(a^2-a+1)`
`ge 3((a^2-a+1)(8sin^2a)/(sqrt((a^2a+1)))(27cosec^2a)/sqrt((a^2-a+1)))^(1/3)`
`=3(2^3 3^3 )^(1/3)=3(6)=18`
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