Question

csc(-x)-sin(-x)=-cosxcotx

Answer 1

csc(-x) * -sin(-x) = -cosx * cotx
1/sin(-x) * -sin(-x) = -cosx * cosx / sinx
-1 = -(cosx)^2/sinx
-sinx = -(cosx)^2
-sinx = -(1-(sinx)^2)
-sinx = -1 + sin^2(x)
sin^2(x) + sin(x) - 1 = 0
Quadratic? Unless I messed up somewhere...
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Answer 2

Ah, sorry, this is a proof that both of the sides are equal?
I'll get back to this if no one else answers.

Answer 3

csc(-x)-sin(-x)=-cscx+sinx=-cos^2x/sinx=-cosxcotx
stands true for all values of x