Question

establish the identity. csc θ·cos θ = cot θ write the left side in terms of sine and cosine. □·cos θ

Explanation:

Step1: Recall csc identity

Recall that $\csc\theta=\frac{1}{\sin\theta}$. So the left - hand side becomes $\frac{1}{\sin\theta}\cdot\cos\theta$.

Step2: Simplify the expression

$\frac{1}{\sin\theta}\cdot\cos\theta=\frac{\cos\theta}{\sin\theta}$.

Step3: Recall cot identity

Since $\cot\theta = \frac{\cos\theta}{\sin\theta}$, the left - hand side $\frac{\cos\theta}{\sin\theta}$ is equal to the right - hand side $\cot\theta$. And the blank should be filled with $\frac{1}{\sin\theta}$.

Answer:

$\frac{1}{\sin\theta}$