We are given that,

cos^-1 x > sin^-1 x

We need to find the range of x.

Using the property of inverse trigonometry,

Or,

So, re-writing the inequality,

cos^-1 x > sin^-1 x

Adding cos^-1 x on both sides of the inequality,

Dividing both sides of the inequality by 2,

Taking cosine on both sides of the inequality,

is the minimum value of x, while the maximum value of cosine function is 1.