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`sec^2 x=(4xy)/(x+y)^2` is true if and only ifA. `x+yne0`B. `x=y,xne0`C. `x=y`D. `xne0,yne0`

Answer» Correct Answer - B
Given, `sec^2theta=(4xy)/((x+y)^2ge1`
Now `sec^2thetage1rArr(4xy)/((x+y)^2ge1`
`or (x+y)^2le4xy`
`or (x+y)^2-4xyle0`
`or (x-y)^2le0`
But for real values of x and y,
`(x-y)^2ge0or(x-y)^2=0`
`:. x=y`
Also `x+yne0rArrxne0.yne0`


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