`1, sin^6\alpha+cos^6\alpha+3sin^2\alpha.cos^2\alpha`
`=(sin^2\alpha+cos^2\alpha)(sin^4\alpha-sin^2\alpha.cos^2\alpha+cos^4\alpha)+3sin^2\alpha.cos^2\alpha`
`=sin^4\alpha-sin^2\alpha.cos^2\alpha+cos^4\alpha+3sin^2\alpha.cos^2\alpha`
`=sin^4\alpha+2sin^2\alpha.cos^2\alpha+cos^4\alpha`
`=(sin^2\alpha+cos^2\alpha)^2`
`=1^2`
`=1`
`2, 2002(sin^6\alpha+cos^6\alpha)-3003(sin^4\alpha+cos^4\alpha)`
`=2002(sin^2\alpha+cos^2\alpha)(sin^4\alpha-sin^2\alpha.cos^2\alpha+cos^4\alpha)-3003[(sin^2\alpha+cos^2\alpha)^2-2sin^2\alpha.cos^2\alpha]`
`=2002(sin^4\alpha-sin^2\alpha.cos^2\alpha+cos^4\alpha)-3003(1-2sin^2\alpha.cos^2\alpha)`
`=2002sin^4\alpha-2002sin^2\alpha.cos^2\alpha+2002cos^4\alpha-3003+6006sin^2\alpha.cos^2\alpha`
`=2002sin^4\alpha+4004sin^2\alpha.cos^2\alpha+2002cos^4\alpha-3003`
`=2002(sin^4\alpha+2sin^2\alpha.cos^2\alpha+cos^4\alpha)-3003`
`=2002(sin^2\alpha+cos^2\alpha)^2-3003`
`=2002.1^2-3003`
`=2002-3003`
`=-1001`
