If cot - 1 ⁡ x 2 - 7 cot - 1 ⁡ x + 10 0 , then the range of x will be

Question

If cot - 1 ⁡ x 2 - 7 cot - 1 ⁡ x + 10 > 0 , then the range of x will be, ( - ∞ , cot ⁡ 2 ), - ∞ , cot ⁡ 5, cot ⁡ 2 , cot ⁡ 5, cot ⁡ 2 , ∞

MARKS App · Accepted Answer

cot - 1 ⁡ x - 5 cot - 1 ⁡ x - 2 > 0 ⇒ cot - 1 ⁡ x ∈ - ∞ , 2 ∪ 5 , ∞ ⇒ cot - 1 ⁡ x ∈ 0 , 2 (Taking intersection with range of cot − 1 x ) ⇒ n ∈ ( cot ⁡ 2 , ∞ )

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