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

Explanation

Given expression, `3(sinx-cos)^(4)+6(sinx+cosx)^(2)+4(sin^(6)x+cos^(6)x)`
`" "=3[sin^(2)x+cos^(2)x-2sinxcosx]^(2)+6[sin^(2)x+cos^(2)x+2*sinx*cosx]+4[(sin^(2)x)^(3)+(cos^(2)x)^(3)]`
`" "=3(1-sin2x)^(2)+6(1+sin2x)+4[(sin^(2)+cos^(2)x)(sin^(4)x-sinxcos^(2)x+cos^(4)x)`
`" "=3(1-sin^(2)23x-2sin2x)+6+6sin2x+4[(sin^(2)x+cos^(2)x)^(2)3sincos^(2)x]`
`" "=3+3sin^(2)2x-6sin2x+6+6sin2x`
`" "=4-3sin^(2)2x=13`