$5.27 \sin ^{2}\left(\frac{\pi}{8}+t\right)=\sin t+\sin ^{2}\left(\frac{\pi}{8}-t\right)$.
5.27 Instruction. Use the power reduction formula (4.16).

Omвem: $t_{1}=\pi k k_{2}=\frac{\pi}{4}(8 k \pm 1), k \in Z$.