Question

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

Answer 1

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.