Simplify cot^2(x) - csc^2(-x)

Question

This was a multiple choice question, the answer i got was 1, but apparently the answer was -1, how could this be since csc^2(-x) = -csc^2x which would turn the subtraction into positive?

Answer 1

cot²x - csc²(-x) = cos²x/sin²x - 1/sin²(-x)

 

=  cos²x/sin²x - 1/(-sinx)² =  cos²x/sin²x - 1/sin²x

 

= (cos²x - 1)/sin²x = -sin²x/sin²x = -1