Answer:
- [tex]\frac{1}{2}[/tex][tex]\sqrt{2+\sqrt{3} }[/tex]
Step-by-step explanation:
Using the half angle formula
• cos([tex]\frac{x}{2}[/tex]) = [tex]\sqrt{\frac{1+cosx}{2} }[/tex]
here [tex]\frac{x}{2}[/tex] = [tex]\frac{11\pi }{12}[/tex], hence
x = [tex]\frac{11\pi }{6}[/tex]
and cos ([tex]\frac{11\pi }{6}[/tex]) = cos([tex]\frac{\pi }{6}[/tex]) = [tex]\frac{\sqrt{3} }{2}[/tex]
cos ([tex]\frac{11\pi }{12}[/tex])
= - [tex]\sqrt{\frac{1+\frac{\sqrt{3} }{2} }{2} }[/tex]
= - [tex]\sqrt{\frac{2+\sqrt{3} }{4} }[/tex] = - [tex]\frac{1}{2}[/tex][tex]\sqrt{2+\sqrt{3} }[/tex]
