Answer: option b.
Step-by-step explanation:
You must keep on mind the following identities:
[tex]csc\theta=\frac{1}{sin\theta}\\\\cot\theta=\frac{1}{tan\theta}[/tex]
[tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex]
Therefore, you can simplify the expression given in the problem as you can see below:
- Substitute identities:
[tex]\frac{csc\theta}{cot\theta}=\frac{\frac{1}{sin\theta}}{\frac{1}{tan\theta}}\\\\=\frac{tan\theta}{sin\theta}\\\\=\frac{\frac{sin\theta}{cos\theta}}{sin\theta}\\\\=\frac{sin\theta}{(cos\theta)(sin\theta)}\\\\=\frac{1}{cos\theta}[/tex]
By definition:
[tex]\frac{1}{cos\theta}=sec\theta[/tex]
