If sin inverse of x is greater than cos inverse of x then
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1/√2 < x ≤ 1 if Sin⁻¹x > Cos⁻¹x
Step-by-step explanation:
Sin⁻¹x > Cos⁻¹x
=> Sin(Sin⁻¹x) > Sin(Cos⁻¹x)
=> x > √(1 - x²)
=> x² > 1 - x²
=> 2x² > 1
=> x² > 1/2
=> x > 1/√2
but x can not be greater than 1
hence 1/√2 < x ≤ 1
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