13. verify the identity. justify each step.

To solve this problem you must apply the proccedure shown below:
 1. You have: 
 (secθ/cscθ-cotθ)-(secθ/cscθ+cotθ)
 2.Substract both expressions, as following:
 secθcscθ+secθcotθ-secθcscθ+secθcotθ/(cscθ-cotθ)(cscθ+cotθ)
 3. Simpliying:
 (2secθcotθ)/(cscθ-cotθ)(cscθ+cotθ)
 4.Let's solve the numerator and then the denominator:
 The numerator:
 (2secθcotθ)=(2/cosθ)(cosθ/sinθ)=2cosθ/(cosθ)(sinθ)=2/sinθ
 The denominator:
 (cscθ-cotθ)(cscθ+cotθ)=(1/sinθ-cosθ/sinθ)(1/sinθ+cosθ/sinθ)=(1-cosθ/sinθ)(1+cosθ/sinθ)=1-cos^2θ/sin^2θ=sin^2θ/sin^2θ=1
 5. Let's susbtitute the numerator and the denominator:
 (2/sinθ)/1=2/sinθ=2cscθ