$y=15-4sin\dfrac{x}{2}.cos\dfrac{x}{2}$
$\Leftrightarrow y= 15- 2sinx$
Lại có : `- 1 <= sinx <= 1`
$\Leftrightarrow$ `- 2 <= 2sinx <= 2`
$\Leftrightarrow$ `- 2 <= - 2sinx <= 2`
$\Leftrightarrow$ `13 <= 15-2sinx <= 17`
$\to y_{max} = 17 \Leftrightarrow sinx =1$
$\Leftrightarrow x = \dfrac{\pi}{2} + k2\pi ( k \in \mathbb{Z})$
$\to y_{min} = 13 \Leftrightarrow sinx =-1$
$\Leftrightarrow x = \dfrac{3\pi}{2} + k2\pi (k \in \mathbb{Z})$
