Answer:
x = [tex]\frac{2\pi }{3}[/tex], x = [tex]\frac{4\pi }{3}[/tex]
Step-by-step explanation:
using the trigonometric identity
• sec x = [tex]\frac{1}{cosx}[/tex]
isolate sec x by subtracting 6 from both sides and dividing both sides by 2
2sec x = - 4 ⇒ sec x = - 2, hence
[tex]\frac{1}{cosx}[/tex] = - 2
⇔ cosx = - [tex]\frac{1}{2}[/tex]
since cos x < 0 then x is in second/ third quadrant
x = [tex]\frac{2\pi }{3}[/tex] or x = [tex]\frac{4\pi }{3}[/tex]
