Answer: 45 is a counterexample of the expression
Given:
[tex]\frac{\text{ sec }\theta}{\tan\theta}=\sin\theta[/tex]Let us first write sec and tan in terms of cos and sin functions:
[tex]\begin{gathered} \frac{\text{sec}\theta}{\tan\theta}=\frac{\frac{1}{\cos\theta}}{\frac{\sin\theta}{\cos\theta}} \\ \Rightarrow\frac{1}{\cos\theta}\times\frac{\cos\theta}{\sin\theta} \\ =\frac{1}{\sin\theta} \end{gathered}[/tex]We now have:
[tex]\frac{1}{\sin\theta}=\sin\theta[/tex]As we can see, the two expressions are not equal, therefore:
[tex]\begin{gathered} \frac{1}{\sin(\theta)}\ne\sin(\theta) \\ \frac{1}{\sin(45)}\sin(45) \end{gathered}[/tex]Since the two expressions are not equal, 45 is a counterexample of the expression.
