Question

Consider the expression 2√ 3 cos(x)csc(x)+4cos(x)-3csc(x)-2 √ 3 This expression can be represented as the product of the factors...

Answer 1

The answer:
let be A(x) =2√ 3 cos(x)csc(x)+4cos(x)-3csc(x)-2 √ 3

this function can be represented as the product of the factors

proof   
2√ 3 cos(x)csc(x)+4cos(x)-3csc(x)-2 √ 3 = 

2√ 3 cos(x)csc(x)+4cos(x)csc(x) / csc(x) -  3csc(x)- 2 √ 3 csc(x) / csc(x)
this method doesn't change nothing inside the function A(x)

so we have 
[ 2√ 3 cos(x) +4cos(x) / csc(x) -  3 - 2 √ 3 / csc(x) ]  . csc(x)  this is a product of two factors, 
[ 2√ 3 cos(x) +4cos(x) / csc(x) -  3 - 2 √ 3 / csc(x) ]  and csc(x) 

for more explanation

A(x) =[ 2√ 3 cos(x) - 3 + (4cos(x) - 2 √ 3 ) / csc(x)  ]  . csc(x)