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
