Chapter 6 - Section 6.2 - More on Trigonometric Equations - 6.2 Problem Set - Page 334: 72

( d )

$csc(\theta)-2cot(\theta)=0$ $\frac{1}{sin(\theta)}-2\frac{cos(\theta)}{sin(\theta)}=0\;\;\;\;\;\;\;\;\;$Multiply by $sin(\theta)$ $1-2cos(\theta)=0$ $2cos(\theta)=1$ $cos(\theta)=\frac{1}{2}$ So choice $(d)$ is the right solution because when solved the equation step by step we found $cos(\theta)=\frac{1}{2}$.