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Sagot :
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]
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