Simplify the first trigonometric expression by writing the simplified form in terms of the second expression (1/1-/1+cos); cscx

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