[tex] \Large{\mathbb{SOLUTION:}}[/tex]
Based on the given conditions:
[tex] \boxed{\rm{\cos^2 60 + \sec 30}}[/tex]
Express the given with sin and cos
[tex] \red{\sec 30 = \frac{1}{\cos30}} \\ \downarrow \\ \cos^2 60 + \frac{1}{\cos30} [/tex]
As we know that:-
- [tex] \cos 60 = \frac{1}{2} [/tex]
- [tex] \cos 30 = \frac{2\sqrt{3}}{2} [/tex]
Substitute it
[tex] \Big(\frac{1}{2}\Big)^2 + \frac{1}{\frac{\sqrt{3}}{2}} [/tex]
[tex] \frac{1}{4} + \frac{2\sqrt{3}}{3}[/tex]
[tex] \therefore [/tex] The exact value is [tex] \frac{1}{4} + \frac{2\sqrt{3}}{3}[/tex].
