Pre-calc

can someone show me how to solve this identity:
csc^4(x)-cot^4(x)=(2csc^2)-1
note: you can only work on one side
additional info: 1+cot^2(x)=csc^2(x), 1+tan^2(x)=sec^2(x)

I am having problems with this one
You have left out an x on the right hand side,
Could you just double check that the rest of the question is written down correctly.
Thanks.

csc^4(x)-cot^4(x)= (2csc^2(x))-1

LHS = [ 1 / (sin ²x) ² ] - [ (cos ²x) ² / (sin ²x) ² ]

= [ 1 - (cos ²x) ² ] / (sin ²x)

= [ (1-cos ²x)(1+cos ²x) ] / (1-cos ²x) ²

= (1+cos ²x) / (1-cos ²x)

= (1+cos ²x) / sin ²x

= (1+1-sin ²x) / sin ²x

= (2-sin ²x) / sin ²x

= 2/sin ²x - sin ²x/sin ²x

= 2csc ²x -1

=RHS QED