3-1/36???
What is the minimum value of 9sec2x + 10cosec2x for all x belongs to R??
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6 Answers
62i had written a lot of stuff here but somehow got delted..
The minimum value will be 19+2√90
Because we have sec2x=tan2+1
The given expression becomes 19+10t2+9/t2
Now apply AM GM On the second and 3rd terms to get 2√90
Hecnce.. 19+2√90
1d answer is 49 but i m getting 49 and 50 both by two different methods!!!
341in that case the function is 9 \sec^2 x + 16 \csc^2 x
If you are familiar with Cauchy Schwarz Inequality,
(\sin^2 x + \cos^2 x) (9 \sec^2 x + 16 \csc^2 x) \ge (3+4)^2 = 49
1no...... i am not.. familiar with that inequality......
i just converted whole equn in terms of tan and sec and then applied AM≥GM... from there i got 49
but on directly applying AM≥GM i m getting 50!!!
so where's the fault??
62surbhi.. I trhink you are making a mistake somewhere...
Is the question that you have given correct..
Even otherwise.
iinequalities dont always mean you will get the correct lowest/ highest value...
For instance ... lets see sin x + 4/sin x (sin x positive)
AM GM will tend to give 4 as the minimum value..
but that will hold only if both terms are equal.. ie sin x =2
Which never holds .. hence minima will never occur..
The correct answer how ever is 1+4=5