If `alpha in (0,pi/2),t h e nsqrt(x^2+x)+(tan^2alpha)/(sqrt(x^2+x))` is always greater than or equal to `2tanalpha` `1` `2` `sec^2alpha`

Options

A. `2tan alpha`
B. 1
C. 2
D. `sec^(2) alpha`

Answer

A

Explanation

Using `A.M.geG.M,` we have
`(1)/(2){sqrt(x^(2)+x)+(tan^(2)alpha)/(sqrt(x^(2)+x))}gesqrt(sqrt(x^(2)+x)xx(tan^(2)alpha)/(sqrt(x^(2)+x)))`
`implies" "sqrt(x^(2)+x)+(tan^(2)alpha)/(sqrt(x^(2)+x))ge2tanalpha`