(7csc(x)+7)(7csc(x)-7)

Question

Can i please get help on how to solve this equation? 

(7csc(x)+7)(7csc(x)-7) 

Answer 1

(7cscx+7)(7cscx-7)

FOIL

49csc²x-49

49(csc²x-1)

csc²x=1+cot²x

substitute

49(1+cot²x-1)

49cot²x seems to be the simplest form although cot=1/tan and cot=cos/sin

or, csc²x-1=cot²x and then substitute to get 49cot²x

Answer 2

(a+b)(a-b) = a^2 - b^2

see: multiply each term

(a+b)(a-b)= a^2 - ab +ba - b^2 two middle value cancel each other

(a+b)(a-b)= a^2 - b^2

 

so 

(7csc(x) + 7)(7csc(x) -7) = 7csc^2(x) - 49

 

csc^2(x) = 1+cot^2(x)

 

7csc^2(x) - 49 = 7(1+cot^2(x)) - 49

                      = 7 + 7cot^2(x) - 49

                      = 7cot^2 - 42

One can continue substitute 

cot(x) = cos(x)/sin(x)

but, doesn't seem to simplify.