Đáp án:
$\left[\begin{array}{l}x = 15^o + k.360^o\\x = 85^o +k.120^o \end{array}\right.\quad (k \in \Bbb Z)$
Giải thích các bước giải:
$\begin{array}{l}\sin(2x - 45^o) + \cos(x + 60^o) = 0\\ \Leftrightarrow \sin(2x - 45^o) = -\cos(x + 60^o)\\ \Leftrightarrow \sin(2x - 45^o) = - \cos(90^o + x - 30^o)\\ \Leftrightarrow \sin(2x - 45^o) = \sin(x-30^o)\\ \Leftrightarrow \left[\begin{array}{l}2x - 45^o = x - 30^o + k.360^o\\2x - 45^o = 210^o - x + k.360^o\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x = 15^o + k.360^o\\x = 85^o +k.120^o \end{array}\right.\quad (k \in \Bbb Z)\end{array}$
