1: \(y=\sqrt{3}\cdot sin^2x-\left(1-sin^2x\right)+5\)
\(=sin^2x\left(\sqrt{3}+1\right)-1+5=sin^2x\left(\sqrt{3}+1\right)+4\)
\(0< =sin^2x< =1\)
=>\(0< =sin^2x\left(\sqrt{3}+1\right)< =\sqrt{3}+1\)
=>4<=y<=căn 3+5
y min=4 khi sin^2x=0
=>sin x=0
=>x=kpi
\(y_{max}=5+\sqrt{3}\) khi \(sin^2x=1\)
=>\(cos^2x=0\)
=>cosx=0
=>\(x=\dfrac{pi}{2}+kpi\)
2: \(y=5\left[\dfrac{3}{5}sinx+\dfrac{4}{5}cosx\right]+7\)
\(=5\cdot\left[sinx\cdot cosa+cosx\cdot sina\right]+7\)(Với cosa=3/5; sin a=4/5)
\(=5\cdot sin\left(x+a\right)+7\)
-1<=sin(x+a)<=1
=>-5<=5sin(x+a)<=5
=>-5+7<=y<=5+7
=>2<=y<=12
\(y_{min}=2\) khi sin (x+a)=-1
=>x+a=-pi/2+kp2i
=>\(x=-\dfrac{pi}{2}+k2pi-a\)
\(y_{max}=12\) khi sin(x+a)=1
=>x+a=pi/2+k2pi
=>\(x=\dfrac{pi}{2}+k2pi-a\)
