27. $\log _{\frac{1}{4}}\left[\log _{4}(\cos 2 x+\sin 2 x)\right]=1$.

In № $28-36$ solve the system of equations:
27. Gradually potentiating, we get $\cos 2 x+\sin 2 x=\sqrt{2}$.

From where $\cos \left(\frac{\pi}{4}-2 x\right)=1 ; \quad x=\frac{\pi}{8}(1-8 k)$.

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