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Let x, y, z be elements from interval [0, 2π] satisfying the inequality (4 + sin 4x)(2 + cot2y)(1 + sin4 z) ≤ 12 sin2z then 

(A)  The number of ordered pairs (x, y) is 4. 

(B)  The number of ordered pairs (y, z) is 8. 

(C)  The number of ordered pairs (z, x) is 8. 

(D)  The number of pairs (y, z) such that z = y is 2.

1 Answer

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Best answer

Correct option (C), (D)

Sin2z + cosec2z ≥ 2, 2 + cot2y ≥ 2, 4 + sin4x ≥ 3

⇒ sin2z = 1, cot2y = 0, sin4x = –1

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