min value

find the min value of

4sin²Î¸+9cosec²Î¸

5 Answers

this is same as 6(2/3 sin²Î¸+3/2 cosec²Î¸)

= 6(t+1/t)

Minimum value is 12...

but t can never be 1

so the minimum will be when t is maximum (from the graph of y=x+1/x) or using derivatives test... (at the end point)

so at t=2/3

so 6(2/3+3/2) = 13

Or use AMâ‰¥G.M

edit : amâ‰¥gm is of no use as we get sin²Î¸ = 3/2

we are supposing that t=1
so if we put
2/3sin²Î¸=1,the value becomes
sin²Î¸=3/2...is that so?

direct am.gm

thanks...AM,Gm will produce no help...the answer 13 is right
thanks sir....

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