Concept:We use the standard identity cos−1x+sin−1x=2π and compare cos−1x with sin−1x.Explanation:The given inequality is:(cos−1x)2−(sin−1x)2>0Factorise using a2−b2=(a+b)(a−b):(cos−1x+sin−1x)(cos−1x−sin−1x)>0Using the identity, cos−1x+sin−1x=2π, we get:2π(cos−1x−sin−1x)>0Since 2π>0, this implies:cos−1x−sin−1x>0Now substitute cos−1x=2π−sin−1x:2π−sin−1x−sin−1x>02π−2sin−1x>0sin−1x<4πThe range of sin−1x is [−2π,2π], so sin−1x<4π gives:−1≤x<21Answer:The correct option is D: −1≤x<21.