which function is equivalent to the inverse of y = sec(x)?\no y = cot⁻¹(x)\no y = cos⁻¹(\\frac{1}{x})\no y =…

which function is equivalent to the inverse of y = sec(x)?\no y = cot⁻¹(x)\no y = cos⁻¹(\\frac{1}{x})\no y = csc⁻¹(x)\no y = sin⁻¹(\\frac{1}{x})

which function is equivalent to the inverse of y = sec(x)?\no y = cot⁻¹(x)\no y = cos⁻¹(\\frac{1}{x})\no y = csc⁻¹(x)\no y = sin⁻¹(\\frac{1}{x})

Answer

Explanation:

Step1: Recall the definition of secant

We know that $\sec(x)=\frac{1}{\cos(x)}$.

Step2: Find the inverse - relationship

Let $y = \sec(x)=\frac{1}{\cos(x)}$. Then, to find the inverse, we first express $x$ in terms of $y$. We have $\cos(x)=\frac{1}{y}$. Taking the inverse - cosine of both sides, $x=\cos^{-1}(\frac{1}{y})$. Interchanging $x$ and $y$, the inverse of $y = \sec(x)$ is $y=\cos^{-1}(\frac{1}{x})$.

Answer:

$y = \cos^{-1}(\frac{1}{x})$