assignment submission & scoring assignment submission for this assignment, you submit answers by questions…
assignment submission & scoring assignment submission for this assignment, you submit answers by questions. assignment scoring your last submission is used for your score. 12. -/2 points details larttrig11 2.3.024. 0/3 submissions used solve the equation. (enter your answers as a comma - separated list. use n as an arbitrary integer. enter your response in radians.) 2 sec²(x) - 2 = 0 x = need help?
Answer
Explanation:
Step1: Isolate $\sec^{2}(x)$
First, add 2 to both sides of the equation $2\sec^{2}(x)-2 = 0$. We get $2\sec^{2}(x)=2$, then divide both sides by 2, so $\sec^{2}(x)=1$.
Step2: Recall the relationship between $\sec(x)$ and $\cos(x)$
Since $\sec(x)=\frac{1}{\cos(x)}$, then $\sec^{2}(x)=\frac{1}{\cos^{2}(x)}$. So, $\frac{1}{\cos^{2}(x)} = 1$, which implies $\cos^{2}(x)=1$.
Step3: Solve for $\cos(x)$
Taking the square - root of both sides of $\cos^{2}(x)=1$, we have $\cos(x)=\pm1$.
Step4: Find the values of $x$
When $\cos(x) = 1$, $x = 2n\pi$, where $n\in\mathbb{Z}$ (the set of all integers). When $\cos(x)=-1$, $x=(2n + 1)\pi$, where $n\in\mathbb{Z}$. Combining these results, $x=n\pi$, $n\in\mathbb{Z}$.
Answer:
$n\pi$