If the maximum value of x which satisfies the inequality sin - 1 ⁡ sin ⁡ x ≥ cos - 1 ⁡ sin ⁡ x for x ∈ π 2 , 2 π is λ , then 2 λ 3 is equal to (take π = 3 .14 )

Question

If the maximum value of x which satisfies the inequality sin - 1 ⁡ sin ⁡ x ≥ cos - 1 ⁡ sin ⁡ x for x ∈ π 2 , 2 π is λ , then 2 λ 3 is equal to (take π = 3 .14 ),

MARKS App · Accepted Answer

Let t = sin ⁡ x From the graphs of sin - 1 ⁡ t and cos - 1 ⁡ t , we know that, sin - 1 ⁡ t ≥ cos - 1 ⁡ t for t ∈ 1 2 , 1 ⇒ sin ⁡ x ∈ 1 2 , 1 Hence, x ∈ π 2 , 3 π 4 Maximum value is 3 π 4 = λ So, 2 λ 3 = π 2 = 1 . 57

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