If c o s - 1 sin ⁡ x ≥ s i n - 1 sin ⁡ x , then the number of integral values of x in the interval x ∈ 0,3 π are

Question

If c o s - 1 sin ⁡ x ≥ s i n - 1 sin ⁡ x , then the number of integral values of x in the interval x ∈ 0,3 π are, 7, 6, 4, 5

MARKS App · Accepted Answer

If c o s - 1 x ≥ s i n - 1 x , then x ∈ - 1 2 , 1 2 {using graph} For given inequality, we must have sin ⁡ x ∈ - 1 2 , 1 2 ⇒ x ∈ n π - π 4 , n π + π 4 , n ∈ Ι Possible integral values of x are 0,3 , 6,7 , 9

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