Question

establish the identity csc θ·cos θ = cot θ write the left side in terms of sine and cosine. 1/sin θ·cos θ write the result from the previous step as a single fraction. (do not simplify)

Explanation:

Step1: Recall csc identity

We know that $\csc\theta=\frac{1}{\sin\theta}$, so the left - hand side is $\frac{1}{\sin\theta}\cdot\cos\theta$.

Step2: Write as single fraction

When we multiply a fraction $\frac{1}{\sin\theta}$ by $\cos\theta$ (which can be written as $\frac{\cos\theta}{1}$), we get $\frac{\cos\theta}{\sin\theta}$.

Answer:

$\frac{\cos\theta}{\sin\theta}$