Respuesta :

The given expression is

[tex]\frac{\csc \theta}{\sec \theta}[/tex][tex]\text{ We know that }csc\theta=\frac{1}{\sin x}\text{ and }\sec \theta=\frac{1}{cos\theta}\text{.}[/tex]

Using the reciprocal, we get

[tex]\frac{\csc\theta}{\sec\theta}=\frac{\frac{1}{\sin\theta}}{\frac{1}{\cos \theta}}[/tex]

[tex]\text{ Use }\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}[/tex]

[tex]\frac{\csc\theta}{\sec\theta}=\frac{1}{\sin\theta}\times\frac{\cos \theta}{1}[/tex][tex]\text{ Use }\frac{\cos\theta}{\sin\theta}=\cot \theta.[/tex]

[tex]\frac{\csc\theta}{\sec\theta}=\cot \theta[/tex]

Hence the answer is

[tex]\cot \theta[/tex]