Move the 5 to the other side:
[tex]2\sec(x)=1-5=-4[/tex]
Divide both sides by 2:
[tex]\sec(x) = -2[/tex]
Recall the definition:
[tex]\sec(x)=-2 \iff \dfrac{1}{\cos(x)}=-2[/tex]
Invert both sides
[tex]\cos(x) = -\dfrac{1}{2}[/tex]
This is true when
[tex]x=\pm \dfrac{\pi}{3}[/tex]
If you need both angles to be in [0,2pi], you can recall
[tex]\cos\left(-\dfrac{\pi}{3}\right) = \cos\left(-\dfrac{\pi}{3}+2\pi\right) = \cos\left(\dfrac{5\pi}{3}\right)[/tex]
So, the solutions are
[tex]x=\dfrac{\pi}{3},\quad x=\dfrac{5\pi}{3}[/tex]
Answer:
2pi/3 and 4pi/3
Step-by-step explanation:
this is the answer according to apex
