(1-sin^6θ-cos^6θ)/(1-sin^4θ-cos^4θ)

1-sin^6θ-cos^6θ=1-[(sin^2θ)^3+(cos^2θ)^3]=1-(sin^2θ+cos^2θ)(sin^4θ-sin^2θcos^2θ+cos^4θ)=1-(sin^4θ-sin^2θcos^2θ+cos^4θ)=1-(sin^4θ+2sin^2θcos^2θ+cos^4θ-3sin^2θcos^2θ)=1-[(sin^2θ+cos...