<s>[INST] Express $\sin\frac{\pi}{8}$ and $\cos\frac{\pi}{8}$ with $\cos\frac{\pi}{4}$ I've been trying with no success expressing this functions.
a) $\sin\frac{\pi}{8}$ with $\cos\frac{\pi}{4}$
b) $\cos\frac{\pi}{8}$ with $\cos\frac{\pi}{4}$
I've tried formula of the double angle ($\sin$ and $\cos$) and the ecuation $\cos^2X+\sin^2X=1$. 
Can anyone point what to use or where to start?
I appreciate it, thanks.

UPDATE
I think this is achived with the half formula as njguliyev and nbubis said.
$$\sin\frac{\pi}{8} = \sin(\frac{1}{2} * \frac{\pi}{4}) = \pm\sqrt\frac{1-\cos\frac{\pi}{4}}{2}$$
$$\cos\frac{\pi}{8} = \cos(\frac{1}{2} * \frac{\pi}{4}) = \pm\sqrt\frac{1+\cos\frac{\pi}{4}}{2}$$
 [/INST] Hint:
You my want to take a look at the half angle formulas.
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