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If x(1),x(2) in (0,(pi)/(2)), then (tan(...

If `x_(1),x_(2) in (0,(pi)/(2))`, then `(tan_(x_(2)))/(tanx_(1))` is (where `x_(1)lt x_(2)`)

A

`lt (x_(1))/(x_(2))`

B

`=(x_(1))/(x_(2))`

C

`ltx_(1) x_(2)`

D

`gt(x_(2))/(x_(1))`

Text Solution

Verified by Experts

The correct Answer is:
D
For `x_(1),x_(2) in (0,(pi)/(2))`, we know `(x)/(tanx)` is decreasing function
`therefore" for "x_(1)lt x_(2) rArr (x_(1))/(tanx_(1))gt (x_(2))/(tanx_(2))`
`rArr" "(tanx_(2))/(tanx_(1))gt (x_(2))/(x_(1))`
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