Solution:
Given the expression:
To simplify, recall from trigonometric identities:
[tex]\begin{gathered} \tan\theta=\frac{\sin\theta}{\cos\theta} \\ \\ sec\theta=\frac{1}{\cos\theta} \\ \\ \sin^2\theta+\cos^2\theta=1 \\ \Rightarrow-\cos^2\theta=\sin^2\theta-1 \\ \\ \frac{1}{\tan\theta}=cot\theta \end{gathered}[/tex]
This implies that
[tex]\begin{gathered} \frac{\sin\theta}{\cos\theta}-(\frac{1}{\cos^2\theta}\times\frac{\cos\theta}{\sin\theta}) \\ =\frac{\sin\theta}{\cos\theta}-\frac{1}{\sin\theta\cos\theta} \\ =\frac{\sin^2\theta-1}{\sin\theta\cos\theta} \\ but\text{ -}\cos^2\theta=\sin^2\theta-1 \\ thus,\text{ we have} \\ \frac{-\cos^2\theta}{\sin\theta\cos\theta} \\ =-\frac{\cos\theta}{sin\theta} \\ =-cot\theta \end{gathered}[/tex]
Hence, the expression is simplified to be
[tex]-cot\theta[/tex]
Hence, the correct option is
