1: \(A=sin^4x-cos^4x-2\cdot sin^2x+1\)
\(=\left(sin^2x-cos^2x\right)\left(sin^2x+cos^2x\right)-2\cdot sin^2x+1\)
\(=sin^2x-cos^2x-2\cdot sin^2x+1\)
\(=1-\left(sin^2x+cos^2x\right)=1-1=0\)
2: \(B=sin^6x+cos^6x+3\cdot sin^2x\cdot cos^2x\)
\(=\left(sin^2x+cos^2x\right)^3-3\cdot sin^2x\cdot cos^2x\left(sin^2x+cos^2x\right)+3\cdot sin^2x\cdot cos^2x\)
\(=1-3\cdot sin^2x\cdot cos^2x+3\cdot sin^2x\cdot cos^2x\)
=1
\(A=sin^4x-cos^4x-2sin^2x+1\)
\(=\left(sin^2x+cos^2x\right)\left(sin^2x-cos^2x\right)-2sin^2x+1\)
\(=sin^2x-cos^2x-2sin^2x+1\)
\(=-\left(sin^2x+cos^2x\right)+1=-1+1=0\)
\(B=sin^6x+cos^6x+3sin^2x.cos^2x\)
\(=\left(sin^2x+cos^2x\right)^3-3sin^2x.cos^2x\left(sin^2x+cos^2x\right)+3sin^2x.cos^2x\)
\(=1-3sin^2x.cos^2x+3sin^2x.cos^2x\)
\(=1\)
