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A counterexample for the expression sec0/tan0=sin0 is 45

User Jonasbb
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Answer: 45 is a counterexample of the expression

Given:


\frac{\text{ sec }\theta}{\tan\theta}=\sin\theta

Let us first write sec and tan in terms of cos and sin functions:


\begin{gathered} \frac{\text{sec}\theta}{\tan\theta}=((1)/(\cos\theta))/((\sin\theta)/(\cos\theta)) \\ \Rightarrow(1)/(\cos\theta)*(\cos\theta)/(\sin\theta) \\ =(1)/(\sin\theta) \end{gathered}

We now have:


(1)/(\sin\theta)=\sin\theta

As we can see, the two expressions are not equal, therefore:


\begin{gathered} (1)/(\sin(\theta))\\e\sin(\theta) \\ (1)/(\sin(45))\sin(45) \end{gathered}

Since the two expressions are not equal, 45 is a counterexample of the expression.

User Arseni Kavalchuk
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