Đáp án:
Giải thích các bước giải:
`sin\ (x+\frac{\pi}{2})=\frac{\sqrt{2}}{2}`
`⇔ sin\ (x+\frac{\pi}{2})=sin\ \frac{\pi}{4}`
`⇔` \(\left[ \begin{array}{l}x+\dfrac{\pi}{2}=\dfrac{\pi}{4}+k2\pi\ (k \in \mathbb{Z})\\x+\dfrac{\pi}{2}=\pi-\dfrac{\pi}{4}+k2\pi\ (k \in \mathbb{Z})\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=-\dfrac{\pi}{4}+k2\pi\ (k \in \mathbb{Z})\\x+\dfrac{\pi}{2}=\dfrac{3\pi}{4}+k2\pi\ (k \in \mathbb{Z})\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=-\dfrac{\pi}{4}+k2\pi\ (k \in \mathbb{Z})\\x=\dfrac{\pi}{4}+k2\pi\ (k \in \mathbb{Z})\end{array} \right.\)
Vậy `S={-\frac{\pi}{4}+k2\pi\ (k \in \mathbb{Z});\frac{\pi}{4}+k2\pi\ (k \in \mathbb{Z})}`
