Remember that sec=1/cos:
[tex]\dfrac{1}{\cos(2x-15)}=1.677[/tex]
Invert both members:
[tex]\cos(2x-15) = \dfrac{1}{1.677}[/tex]
Consider the arccos of both sides:
[tex]\arccos(\cos(2x-15))=\arccos\left(\dfrac{1}{1.677}\right)[/tex]
Arccos and cod simplify:
[tex]2x-15=\arccos\left(\dfrac{1}{1.677}\right)[/tex]
Add 15 to both sides:
[tex]2x=\arccos\left(\dfrac{1}{1.677}\right)+15[/tex]
Divide both sides by 2:
[tex]x=\dfrac{\arccos\left(\dfrac{1}{1.677}\right)+15}{2}[/tex]
