Factor:
4tan^2x-(4)/(cotx)+sinx(cscx)

4tan^(2)x-((4)/(cotx))+sinxcscx 

Multiply -1 by the (4)/(cotx) inside the parentheses. 

4tan^(2)x-(4)/(cotx)+sinxcscx 

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is cotx. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions. 

4tan^(2)x*(cotx)/(cotx)-(4)/(cotx)+sin... 

Complete the multiplication to produce a denominator of cotx in each expression. 

(4tan^(2)xcotx)/(cotx)-(4)/(cotx)+(cot... 

Combine the numerators of all expressions that have common denominators. 

(4tan^(2)xcotx-4+cotxsinxcscx)/(cotx)