Inverse Trigonometric FunctionHard
Question
The solution of the inequality (tan-1 x)2 - 3 tan-1 x + 2 > 0 is -
Options
A.(- ∞, tan 1] υ [tan 2, ∞)
B.(-∞, tan 1]
C.(-∞, - tan 1] υ [tan 2, ∞)
D.[tan 2, ∞)
Solution
(tan-1x)2 - 3tan-1x + 2 ≥ 0
(tan-1x - 1) (tan-1x - 2) ≥ 0
we know that tan-1x ∈
so tan-1x ≥ 2 (not possible) or tan-1x ≤ 1
⇒ x ∈ (-∞, tan1]
(tan-1x - 1) (tan-1x - 2) ≥ 0
we know that tan-1x ∈
so tan-1x ≥ 2 (not possible) or tan-1x ≤ 1
⇒ x ∈ (-∞, tan1]
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