solve the equation for x, where x is restricted to the given inter y = sec x - 2, for x in 0, π/2) ∪ (π/2,π…

solve the equation for x, where x is restricted to the given inter y = sec x - 2, for x in 0, π/2) ∪ (π/2,π x = (use parentheses to clearly denote the argument of each function.

solve the equation for x, where x is restricted to the given inter y = sec x - 2, for x in 0, π/2) ∪ (π/2,π x = (use parentheses to clearly denote the argument of each function.

Answer

Explanation:

Step1: Isolate sec x

Add 2 to both sides of the equation $y = \sec x-2$. $y + 2=\sec x$

Step2: Use inverse - secant function

Since $\sec x=y + 2$ and $x\in[0,\frac{\pi}{2})\cup(\frac{\pi}{2},\pi]$, the inverse - secant function $\text{arcsec}$ can be used. $x=\text{arcsec}(y + 2)$

Answer:

$x=\text{arcsec}(y + 2)$