Find the Inverse sec(x)

Problem

sec(x)

Solution

1. Define the function as y=sec(x) and restrict the domain to [0,π/2)∪(π/2,π] to ensure the function is one-to-one.

2. Swap the variables x and y to begin finding the inverse relationship, resulting in x=sec(y)

3. Solve for y by applying the inverse secant function to both sides of the equation.

4. Express the result using the standard notation for the inverse secant function, which is arcsec(x) or sec(x)(−1)

Final Answer

inverse of *sec(x)=arcsec(x)

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