Answer:
-[tex]\sqrt{\frac{2-\sqrt{2}}{4}[/tex]
Step-by-step explanation:
The cosine half-angle formula is
[tex]cos\frac{\pi }{2}[/tex]=±[tex]\sqrt{\frac{1+cosx}{2} }[/tex]
we can write
[tex]cos \frac{3\pi }{8}[/tex]
as
[tex]cos\frac{\frac{3\pi }{4} }{2}[/tex]
=-[tex]\sqrt{\frac{1+cos\frac{3\pi}{4} }{2}[/tex]
=-[tex]\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}[/tex]
=-[tex]\sqrt{\frac{2-\sqrt{2}}{4}[/tex]
(cosine is negative is in second quadrant)
