Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 208: 30

$$\cot^4x+3\cot^2x+2=(\cot^2x+1)(\cot^2x+2)$$

$$A=\cot^4x+3\cot^2x+2$$ We would rewrite $3\cot^2 x$ into $(\cot^2 x+2\cot^2 x)$. $$A=\cot^4 x+\cot^2x+2\cot^2x+2$$ $$A=\cot^2x(\cot^2x+1)+2(\cot^2x+1)$$ $$A=(\cot^2x+1)(\cot^2x+2)$$