First slide

Properties of ITF

Question

If [tan^–1x]² – 2[tan^–1x] + 1 ≤ 0, where [.] denotes greatest integer ≤ x, x belongs to

Difficult

A

[tan1, tan2)
B

$[\frac{π}{4}, \frac{π}{2}]$
C

[tan1, $\infty$ )
D

none of these

Solution

The given inequation is
[[tan^–1 x] – 1]² ≤ 0
⇒ [tan^–1x]= 1 as [[tan^–1x]– 1]² $≮$ 0
⇒ 1 ≤ tan^–1x < 2
⇒ x ∈[tan 1, tan 2)

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