Question

Is $cot$ equal to $\cos$ by $\sin ?$

Answer 1

Determine if $cot$ equal to $\cos$ by $\sin$

For any angle $\theta$ in a right-angled triangle,

$\tan \left(\theta \right)=\frac{\sin \left(\theta \right)}{\cos \left(\theta \right)}$

Now, we know that $co\tan gent$ is the reciprocal of $\tan gent$, therefore,

$$\begin{gathered} \cot \left(\theta \right)=\frac{1}{\tan \left(\theta \right)} \\ \Rightarrow \cot \left(\theta \right)=\frac{\cos \left(\theta \right)}{\sin \left(\theta \right)} \end{gathered}$$

Hence, we can say that $cot$ equal to $\cos$ by $\sin$.