SOLUTION: find the least value of:- {{{4 sec^2(x) + 9 cosec^2(x)}}}

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Question 627346: find the least value of:- 4+sec%5E2%28x%29+%2B+9+cosec%5E2%28x%29
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
4sec%5E2%28x%29+%2B+9cosec%5E2%28x%29
= %282sec%28x%29+-+3cosec%28x%29%29%5E2+%2B+12sec%28x%29cosec%28x%29

The minimum value of the expression will be obtained when the square term will be zero.
To satisfy that 2sec%28x%29+=+3cosec%28x%29. Thus, the expression reduces to
8sec%5E2%28x%29

This will be minimum when sec%5E2%28x%29 will be minimum which is 1.
Hence, the minimum value of the given expression is 8.