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Consider the following statements: Statement 1: sin⁻¹ ((1)/(√(e))) > tan⁻¹ ((1)/(e)) Statement 2: For any x, y ∈ (0,1), if x > y, then sin⁻¹x > tan⁻¹y.

1. Statement 1 is true, Statement 2 is true, and Statement 2 correctly explains Statement 1.
2. Statement 1 is true, Statement 2 is true, but Statement 2 does not correctly explain Statement 1.
3. Statement 1 is false, Statement 2 is true.
4. Statement 1 is true, Statement 2 is false.

Correct answer: Statement 1 is true, Statement 2 is true, and Statement 2 correctly explains Statement 1.

Solution

For x,y in (0,1) with x>y: asin(x)>x>y>atan(y), so Statement 2 is true. With x=1/sqrt(e) ~ 0.61 > y=1/e ~ 0.37, Statement 2 directly gives Statement 1, so it correctly explains it -> option (a).

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