a/ \(P=sin^2x+cos^2x+cos^2x=1+cos^2x\)
Mà \(0\le cos^2x\le1\Rightarrow1\le P\le2\)
\(P_{min}=1\) khi \(cosx=0\)
\(P_{max}=2\) khi \(cosx=\pm1\)
b/ \(P=8sin^2x+3\left(1-2sin^2x\right)=3+2sin^2x\)
Mà \(0\le sin^2x\le1\Rightarrow3\le P\le5\)
\(P_{min}=3\) khi \(sinx=0\)
\(P_{max}=5\) khi \(sinx=\pm1\)
c/ \(P=\left(sin^2x-cos^2x\right)\left(sin^2x+cos^2x\right)=sin^2x-cos^2x=-cos2x\)
Mà \(-1\le cos2x\le1\Rightarrow-1\le P\le1\)
\(P_{min}=-1\) khi \(cos2x=1\)
\(P_{max}=1\) khi \(cos2x=-1\)
d/ \(P=\left(sin^2x+cos^2x\right)^3-3sin^2x.cos^2x\left(sin^2x+cos^2x\right)\)
\(=1-3sin^2x.cos^2x=1-\frac{3}{4}\left(2sinx.cosx\right)^2=1-\frac{3}{4}sin^22x\)
Mà \(0\le sin^22x\le1\Rightarrow\frac{1}{4}\le P\le1\)
\(P_{min}=\frac{1}{4}\) khi \(sin2x=\pm1\)
\(P_{max}=1\) khi \(sin2x=0\)
