Đáp án:
\(x = - 1 - a + \dfrac{\pi }{2} + k2\pi \)
Giải thích các bước giải:
\(\begin{array}{l}
3\sin \left( {x + 1} \right) + 4.\cos \left( {x + 1} \right) = 5\\
\to \dfrac{3}{5}\sin \left( {x + 1} \right) + \dfrac{4}{5}.\cos \left( {x + 1} \right) = 1\\
Đặt:\left\{ \begin{array}{l}
\dfrac{3}{5} = \cos a\\
\dfrac{4}{5} = \sin a
\end{array} \right.\\
Pt \to \sin \left( {x + 1} \right).\cos a + \sin a.\cos \left( {x + 1} \right) = 1\\
\to \sin \left( {x + 1 + a} \right) = 1\\
\to x + 1 + a = \dfrac{\pi }{2} + k2\pi \\
\to x = - 1 - a + \dfrac{\pi }{2} + k2\pi \left( {k \in Z} \right)
\end{array}\)
