`a)`
`VT=(sin^2 alpha - cos^2 alpha)/(1-2sin alpha . cos alpha)`
`=((sin alpha-cos alpha)(sin alpha+cos alpha))/(sin^2 alpha+cos^2 alpha-2sin alpha . cos alpha)`
`=((sin alpha-cos alpha)(sin alpha+cos alpha))/((sin alpha-cos alpha)^2)`
`=(sin alpha+cos alpha)/(sin alpha-cos alpha)=VP`
`to đpcm`
`b)`
`sin^6 alpha + cos^6 alpha + 3 sin^2 alpha . cos^2 alpha`
`=sin^6 alpha + cos^6 alpha + 3 sin^2 alpha . cos^2 alpha . (sin^2 alpha+cos^2 alpha)`
`=sin^6 alpha + cos^6 alpha + 3 sin^4 alpha . cos ^2 alpha+3sin^2 alpha . cos^4 alpha`
`=(sin^2 alpha + cos^2 alpha)^3`
`=1`
