Does this property holds for inverse too? (part- lV)

Calculus Level 3

1 cos 1 ( x ) = sec 1 ( x ) \large \frac{1}{\cos^{-1}(x)} = \sec^{-1} (x)

Determine the number of real solution of x x which satisfy the equation above.

Original problem.
3 \infty 1 2 0

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