Simplifying Using Trig Identities

Question

The expression csc^2(x)-1 is equivalent to 

Answer 1

Or you can just recognize the identity

 

cot²x + 1 = csc²x

 

 

Manipulating it gives you

 

cot²x = csc²x - 1

Answer 2

csc²x - 1 = 1/sin²x - 1 

 

              = (1 - sin²x) / sin²x

 

              = cos²x / sin²x = cot²x