From the given information, you are to show that the product of secθ and cot θ is equivalent to cosecθ that is:
[tex]\sec \theta cot\theta=co\sec \theta[/tex]According to trigonometry identity:
[tex]\begin{gathered} sec\theta=\frac{1}{\cos\theta} \\ cot\theta=\frac{\cos \theta}{\text{sin}\theta} \\ co\sec \theta=\frac{1}{\sin \theta} \end{gathered}[/tex]
Starting from the LHS, we will substitute the given identity into the expression given.
[tex]\begin{gathered} \sec \theta cot\theta=\frac{1}{\cancel{\cos\theta}}\frac{\cancel{\cos \theta}^1}{\sin \theta} \\ \sec \theta cot\theta=1\cdot\frac{1}{\sin \theta} \\ \sec \theta cot\theta=\frac{1}{\sin \theta} \\ \sec \theta cot\theta=\text{cosec}\theta\text{ (Proved)} \end{gathered}[/tex]
