Đáp án:
\(A = 2\sqrt2\cos\dfrac{x}{2}\sin\left(\dfrac{x}{2} + \dfrac{\pi}{4}\right)\)
Giải thích các bước giải:
\(\begin{array}{l}
\quad A = \sin x + \cos x + 1\\
\to A = 2\sin\dfrac{x}{2}\cos\dfrac{x}{2} + 2\cos^2\dfrac{x}{2} - 1 + 1\\
\to A = 2\sin\dfrac{x}{2}\cos\dfrac{x}{2} + 2\cos^2\dfrac{x}{2}\\
\to A = 2\cos\dfrac{x}{2}\left(\sin\dfrac{x}{2} + \cos\dfrac{x}{2}\right)\\
\to A = 2\cos\dfrac{x}{2}\cdot \sqrt2\sin\left(\dfrac{x}{2} + \dfrac{\pi}{4}\right)\\
\to A = 2\sqrt2\cos\dfrac{x}{2}\sin\left(\dfrac{x}{2} + \dfrac{\pi}{4}\right)\\
\end{array}\)
