## Trigonometry (11th Edition) Clone

$$\frac{\sec x}{\csc x}=\tan x$$ $\text{E}$ is the answer.
$$A=\frac{\sec x}{\csc x}$$ 2 Reciprocal Identities related to $\sec\theta$ and $\csc\theta$ state that $$\sec\theta=\frac{1}{\cos\theta}$$ $$\csc\theta=\frac{1}{\sin\theta}$$ That means we can rewrite $A$ as follows: $$A=\frac{\frac{1}{\cos x}}{\frac{1}{\sin x}}$$ $$A=\frac{\sin x}{\cos x}$$ Also, from Quotient Identities, we know $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$ Therefore, $$A=\tan x$$ $\text{E}$ is the answer.