Đáp án:
\(\begin{array}{l}
a)\quad S = \left\{k\pi\ \Big|\ k\in \Bbb Z\right\}\\
b)\quad S = \left\{\dfrac{5\pi}{8} + k\pi\ \Bigg|\ k\in\Bbb Z\right\}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\quad \tan\left(x + \dfrac{\pi}{4}\right) = 1\qquad (*)\\
ĐK:\cos\left(x + \dfrac{\pi}{4}\right)\ne 0\Leftrightarrow x \ne \dfrac{\pi}{4} + n\pi\\
(*) \Leftrightarrow x + \dfrac{\pi}{4} = \dfrac{\pi}{4} + k\pi\\
\Leftrightarrow x = k\pi\quad (k\in\Bbb Z)\\
\text{Vậy}\ S = \left\{k\pi\ \Big|\ k\in \Bbb Z\right\}\\
b)\quad \cos\left(2x -\dfrac{\pi}{4}\right)=-1\\
\Leftrightarrow 2x - \dfrac{\pi}{4}=\pi + k2\pi\\
\Leftrightarrow x = \dfrac{5\pi}{8} + k\pi\quad (k\in\Bbb Z)\\
\text{Vậy}\ S = \left\{\dfrac{5\pi}{8} + k\pi\ \Bigg|\ k\in\Bbb Z\right\}
\end{array}\)
