Evaluate the determinants.
∣∣∣x2−x+1x−1x+1x+1∣∣∣
∣∣∣x2−x+1x−1x+1x+1∣∣∣=(x2−x+1)(x+1)−(x+1)(x−1)=x3−x2+x+x2−x+1−(x2−1)=x3+1(x2−1)=x3−x2+2
∣∣∣cosθ−sinθsinθcosθ∣∣∣
∣∣ ∣ ∣∣1xx2x21xxx21∣∣ ∣ ∣∣=(1−x3)2
Evaluate: ∣∣∣x2−x+1x−1x+1x+1∣∣∣