find the exact value of the expression. sec^(-1)(1) select the correct choice below and, if necessary, fill…

find the exact value of the expression. sec^(-1)(1) select the correct choice below and, if necessary, fill in the answer box to complete you a. sec^(-1)(1)= (simplify your answer. type an exact answer, using π as needed. use integers c b. there is no solution.

find the exact value of the expression. sec^(-1)(1) select the correct choice below and, if necessary, fill in the answer box to complete you a. sec^(-1)(1)= (simplify your answer. type an exact answer, using π as needed. use integers c b. there is no solution.

Answer

Explanation:

Step1: Recall secant - inverse secant relationship

The inverse secant function (y = \sec^{-1}(x)) is defined such that (\sec(y)=x) and (y\in[0,\frac{\pi}{2})\cup(\frac{\pi}{2},\pi]). We know that (\sec(y)=\frac{1}{\cos(y)}), and we want to find (y) when (x = 1), so (\frac{1}{\cos(y)}=1).

Step2: Solve for (y)

If (\frac{1}{\cos(y)}=1), then (\cos(y)=1). In the domain (y\in[0,\frac{\pi}{2})\cup(\frac{\pi}{2},\pi]), when (\cos(y) = 1), (y = 0).

Answer:

A. (\sec^{-1}(1)=0)