[tex]cos^2x-4sinx = 1-sin^2 x-4sinx = -sin^2x-4sinx+1 \\ \\ \boxed{1}\quad -1\leq sinx \leq 1 \Big|^2 \Rightarrow sin^2x \leq1 \Big|\cdot(-1) \Rightarrow \boxed{-sin^2x \geq -1} \\ \\ \boxed{2} \quad -1\leq sinx \leq 1 \Big|\cdot(-4) \Rightarrow 4 \geq -4sinx \geq -4 \Rightarrow \boxed{-4sinx \geq -4}\\ \\ $Adunam cele 2 inegalitati: $ \Rightarrow -sin^2 x -4sinx \geq -1-4 \R \Rightarrow \\ \\ \Rightarrow -sin^2 x-4sinx\geq -5 \Big|+1 \Rightarrow -sin^2 x-4sinx+1 \geq -5+1 \Rightarrow [/tex]
[tex]\Rightarrow -sin^2 x-4sinx+1 \geq -4 \Leftrightarrow cos^2x -4sinx \geq -4 \\ \\ \rightarrow $ minimul expresiei este -4 [/tex]
