cscx is 1/sinx
maybe they want us to use pythagorean identity
I notice we have 1-cos(x) and 1+cos(x), if we multiply them, we get
and if we look at the pythagorean identity and minus cos^2(x) from both sides, we get
since ,
(recall that (a-b)(a+b)=a²-b²)
match the denomenators of the original fraction
multiply first fraction by and the 2nd by
, hmm, to get ride of those cos(x)
look to the pythagorean identity again
, force one side into form 1+cos^2(x)
, recall that since csc(x)=1/sin(x), sin(x)=1/csc(x) and sin^2(x)=1/(csc^2(x))
subsituting
distributing
is the simplified expression