\(y=2-sin^2x-sin^2\left(m+x\right)-2cosm.cosx.cos\left(m+x\right)\)
\(=cos^2x+cos^2\left(m+x\right)-2cosm.cosx.cos\left(m+x\right)\)
\(=cos^2x+\left[cos\left(m+x\right)-2cosm.cosx\right].cos\left(m+x\right)\)
\(=cos^2x+\left[cosm.cosx-sinm.sinx-2cosm.cosx\right].cos\left(m+x\right)\)
\(=cos^2x-\left[sinm.sinx+cosm.cosx\right].cos\left(m+x\right)\)
\(=cos^2x-cos\left(m-x\right).cos\left(m+x\right)\)
\(=cos^2x-\dfrac{1}{2}\left(cos2m+cos2x\right)\)
\(=cos^2x-\dfrac{1}{2}cos2x-\dfrac{1}{2}cos2m\)
\(=cos^2x-\dfrac{1}{2}\left(2cos^2x-1\right)-\dfrac{1}{2}cos2m\)
\(=\dfrac{1}{2}-\dfrac{1}{2}cos2m\)
\(\Rightarrow\) Hàm số \(y=2-sin^2x-sin^2\left(m+x\right)-2cosm.cosx.cos\left(m+x\right)\) nhận giá trị không đổi trên R.
