Tính: `3(sin^8 x -cos^8 x)+4(cos^6 x - 2sin^6 x)+6sin^4 x`

`3(sin^8x - cos^8x) + 4(cos^6x - 2sin^6x) + 6sin^4x `

`= 3(sin^4x + cos^4x)(sin^2x + cos^2x)(sin^2x - cos^2x) + 4(cos^6x - 2sin^6x) + 6sin^4x`

`= 3(sin^4x + cos^4x)(sin^2x - cos^2x) + 4(cos^6x - 2sin^6x) + 6sin^4x`

`= 3sin^6x - 3sin^4xcos^2x + 3cos^4sin^2x - 3cos^6x + 4cos^6x - 8sin^6x + 6sin^4x`

`= -5sin^6x + cos^6x - 3sin^4x(1 - sin^2x) + 3cos^4x(1 - cos^2x) + 6sin^4x`

`= -5sin^6x + cos^6x - 3sin^4x+ 3sin^6x + 3cos^4x- 3cos^6x + 6sin^4x`

`= 3(sin^4x + cos^4x) - 2(sin^6x + cos^6x)`

`= 3(1 - 2sin^2x cos^2x) - 2(1 - 3sin^2x.cos^2x)`

`=3 - 6sin^2x cos^2x - 2 + 6sin^2x.cos^2x`

`= 1`