Respuesta :
In the question, we are asked to prove that
[tex]\sec \theta\cot \theta=\csc \theta[/tex]We can find the proof below.
Explanation
To find the proof we must recall some fundamental principles of trigonometry.
[tex]\begin{gathered} 1)\sec \theta=\frac{1}{\sin \theta} \\ 2)\cot \theta=\frac{\cos \theta}{\sin \theta} \\ 3)\frac{1}{\cos\theta}=\csc \theta \end{gathered}[/tex]We will then simplify the left-hand side. If it gives the same value as the right-hand side, it implies that the proof is complete.
Therefore, from the left-hand side,
Proof
[tex]\begin{gathered} \sec \theta\cot \theta=\frac{1}{\cos \theta}\times\frac{\cos\theta}{\sin\theta}=\frac{1}{\text{sin}\theta} \\ =\csc \theta \end{gathered}[/tex]Since the left-hand side has been proven to be equal to the right-hand side when simplified, that concludes the prove
