Answer:
No. The reciprocal of a function is rarely the same as the inverse of the function.
Explanation:
tan^1(a) signifies the arctangent function, the function that returns the angle for a given tangent value of a.
tan(a)^-1 signifies the reciprocal of the tangent function, which is the definition of the cotangent function.
The attached graph compares the two functions.