The complete solution set of the inequality - -1 x -2-6- -1 x -9 - 0- where - denotes greatest integer function isA- - 2B- - 3C- 2- 3D- 2- -

The correct option is B ( ∞, cot3)[cot^ 1x]^2 6[cot^ 1x]+9 ≤ 0 ⇒ ([cot^ 1x] 3)^2 ≥ 0 ∴ [cot^ 1x]=3 ⇒ 3 ≤ cot^ 1x lt;4 x ∈ ( ∞, cot3) ...

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General Solution of Trigonometric Equation

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Question

The complete solution set of the inequality $[c o t^{- 1} x]^{2} - 6 [c o t^{- 1} x] + 9 \leq 0,$ where $[.]$ denotes greatest integer function is

$(- \infty, c o t 2)$

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$(- \infty, c o t 3)$

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$(c o t 2, c o t 3)$

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$(c o t 2, \infty)$

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The complete solution set of the inequality $[c o t^{- 1} x]^{2} - 6 [c o t^{- 1} x] + 9 \leq 0,$ where $[.]$ denotes greatest integer function is

[c o s^{- 1} x]^{2} - 6 [c o t^{- 1} x] + \leq 0

[{cot}^{- 1} x] + 2 [{tan}^{- 1} x] = 0

[.]

({tan}^{- 1} x) ({cot}^{- 1} x) - ({tan}^{- 1} x) (1 + \frac{π}{2}) - 2 {cot}^{- 1} x + 2 (1 + \frac{π}{2}) > lim y \to - \infty [{sec}^{- 1} y - \frac{π}{2}]

\begin{matrix} I n v e r s e T r i g o n o m e t r i c & D o m a i n & R a n g e F u n c t i o n y = s i n^{- 1} x & x ϵ [- 1, 1] & y ϵ [\frac{- π}{2}, \frac{π}{2}] y = c o s^{- 1} x & x ϵ [- 1, 1] & y ϵ [0, π] y = t a n^{- 1} x & x ϵ R & y ϵ (\frac{- π}{2}, \frac{π}{2}) y = c o t^{- 1} x & x ϵ R & y ϵ (0, π) y = s e c^{- 1} x & x ϵ R - (- 1, 1) & y ϵ [0, π] - {\frac{π}{2}} y = c o s e c^{- 1} x & x ϵ R - (- 1, 1) & y ϵ [\frac{- π}{2}, \frac{π}{2}] \end{matrix}

[c o t^{- 1} x]^{2} - 6 [c o t^{- 1} x] + 9 \leq 0

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