(1-cos^2(x)) csc^2(x)=1
one of the trigonometry rules is sin^2(x) + cos^2(x) = 1 if you rearrange this you realize that sin^2= 1-cos^2(x)
we also know that csc^2(x)= 1/sin^2(x) so now you can rewrite your equation as:
sin^2(x) x 1/sin^2(x) = 1
sin^2(x)/sin^2(x) =1
the LHS (left hand side) can cancel down to 1 because the numerator and denominator are the same
so then 1=1 Therefore LHS=RHS
Hope this helps
