`=sin^6a+cos^6a+3sin^2a-cos^2a`
`= (sin^2a )^3+ (cos^3a )^2+3sin^2a-cos^2a`
`= (sin^2a+cos^2a )^3-3sin^2a.cos^2a (sin^2a+cos^2a )+3sin^2a-cos^2a`
`=1-3sin^2a.cos^2a+3sin^2a-cos^2a`
`=3sin^2a-3sin^2a.cos^2a+1-cos^2a`
`=3sin^2a (1-cos^2a )+ (1-cos^2a )`
`= (3sin^2a+1 ) (1-cos^2a )`
`= (3sin^2a+1 ) (sin^2a )=3sin^4a+sin^2a`