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If alpha in (0,pi/2),t h e nsqrt(x^2+x)+...

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`

A

`2 tan alpha`

B

1

C

2

D

`sec^(2) alpha`

Text Solution

Verified by Experts

The correct Answer is:
A
Here, `alpha in (0, (pi)/(2)) rArr tan alpha gt 0`
`:. (sqrt(x^(2) + x) + (tan^(2) alpha)/(sqrt(x^(2) + x)))/(2) ge sqrt(sqrt(x^(2) +x).(tan^(2) alpha)/(sqrt(x^(2) + x)))` [ using AM `ge` GM]
`rArr sqrt(x^(2) + x) + (tan^(2) alpha)/(sqrt(x^(2) + x)) ge 2 tan alpha`
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