Step 1 \((2\sin(x)\cot(x)+\sin(x)-4\cot(x)-2)/(2\cot(x)+1)= Factor\ 2\sin(x)\cot(x)+\sin(x)-4\cot(x)-2: (-2+\sin(x))(2\cot(x)+1) =((-2+\sin(x))(2\cot(x)+1))/(2\cot(x)+1)=2+\sin(x)\) Hence, given equation is true.

Step 2

Factors of \(2\sin(x)\cot(x)+\sin(x)-4\cot(x)-2 is =2\cot(x)\sin(x)-2 \cdot 2\cot(x)-2 =2\cot(x)(\sin(x)-2)+\sin(x)-2 =2(-2+\sin(x))\cot(x)+1\cdot (-2+\sin(x)) =(-2+\sin(x))(2\cot(x)+1) (2\sin(x)\cot(x)+\sin(x)-4\cot(x)-2)/(2\cot(x)+1)=-2+\sin(x)\)