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Question:

All x satisfying the inequality (cot x)² - 7(cot x) + 10 > 0, lie in the interval:-

(-∞, cot 2)∪(cot 5, ∞)

(-∞, cot 5)∪(cot 4, cot 2)

(cot 5, cot 4)

(cot 2, ∞)

Solution:

Let cot x = t
Then t² - 7t + 10 > 0
On factorizing, (t - 2)(t - 5) > 0
cot x = 2, 5
x = cot⁻¹2, cot⁻¹5
On plotting the x on wavy curve we get
x lie in (-∞, cot 2)∪(cot 5, ∞)