Answer:
- [tex]\frac{\sqrt{2-\sqrt{2} } }{2}[/tex]
Step-by-step explanation:
Note that [tex]\frac{5\pi }{8}[/tex] is in the second quadrant
where cos < 0 , hence overall sign will be negative
Using the half- angle formula
cos [tex]\frac{5\pi }{8}[/tex]
= - [tex]\sqrt{\frac{1+cos\frac{5\pi }{4} }{2} }[/tex]
= - [tex]\sqrt{\frac{1-\frac{\sqrt{2} }{2} }{2} }[/tex]
= - [tex]\sqrt{\frac{2-\sqrt{2} }{4} }[/tex]
= - [tex]\frac{\sqrt{2-\sqrt{2} } }{2}[/tex]
