Giải pt: sin x = cos ( x+pi/3)

Đáp án: $x = \dfrac{\pi }{2} - k\pi \left( {k \in Z} \right)$

Giải thích các bước giải:

$\begin{array}{l}
\sin x = \cos \left( {x + \dfrac{\pi }{3}} \right)\\
 \Leftrightarrow \cos \left( {\dfrac{\pi }{2} - x} \right) = \cos \left( {x + \dfrac{\pi }{3}} \right)\\
 \Leftrightarrow \left[ \begin{array}{l}
\dfrac{\pi }{2} - x = x + \dfrac{\pi }{3} + k2\pi \\
\dfrac{\pi }{2} - x =  - x - \dfrac{\pi }{3} + k2\pi 
\end{array} \right.\left( {k \in Z} \right)\\
 \Leftrightarrow \left[ \begin{array}{l}
2x = \dfrac{\pi }{2} - \dfrac{\pi }{3} - k2\pi \\
\dfrac{\pi }{2} =  - \dfrac{\pi }{3} + k2\pi \left( {ktm} \right)
\end{array} \right.\left( {k \in Z} \right)\\
 \Leftrightarrow 2x = \dfrac{\pi }{6} - k2\pi \left( {k \in Z} \right)\\
 \Leftrightarrow x = \dfrac{\pi }{{12}} - k\pi \left( {k \in Z} \right)\\
Vậy\,x = \dfrac{\pi }{2} - k\pi \left( {k \in Z} \right)
\end{array}$