If sin - 1 ⁡ x 4 - 2 sin - 1 ⁡ x 2 + 1 ≤ 0 , then (where, . represents the greatest integral part of x )

Question

If sin - 1 ⁡ x 4 - 2 sin - 1 ⁡ x 2 + 1 ≤ 0 , then (where, . represents the greatest integral part of x ), x ∈ sin ⁡ 1 , sin ⁡ 2 ∪ - 1 , 0, x ∈ - sin ⁡ 1 , 0 ∪ sin ⁡ 1 , 1, x ∈ sin ⁡ 1 , 1 ∪ - sin ⁡ 1 , 0, x ∈ - sin ⁡ 1 , sin ⁡ 2

MARKS App · Accepted Answer

sin - 1 ⁡ x 2 - 1 2 ≤ 0 ⇒ sin - 1 ⁡ x 2 - 1 = 0 ⇒ sin - 1 ⁡ x = 1 , - 1 ⇒ 1 ≤ sin - 1 ⁡ x 2 or - 1 ≤ sin - 1 ⁡ 0 but sin - 1 ⁡ x ∈ - π 2 , π 2 ∴ 1 ≤ sin - 1 ⁡ x ≤ π 2 or - 1 ≤ sin - 1 ⁡ x 0 ⇒ x ∈ - sin ⁡ 1 , 0 ∪ sin ⁡ 1 , 1

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