Simplify this trigonometric equation (identities) Please simplify these trigonometric identities and describe step by step (wording).
$\frac{\sec \theta-\csc \theta}{1-\cot\theta}$

Let $A = \frac{\sec\theta - \csc\theta}{1-\cot\theta}$
$A = \frac{\frac{1}{\cos\theta}-\frac{1}{\sin\theta}}{1-\frac{\cos\theta}{\sin\theta}}$
Now we make common denominators like so:
$A = \frac{\frac{\sin\theta}{\sin\theta \cdot \cos\theta}-\frac{\cos\theta}{sin\theta\cdot \cos\theta}}{\frac{\sin\theta}{\sin\theta}-\frac{\cos\theta}{\sin\theta}}$
$A = \frac{\sin\theta - \cos\theta}{\sin\theta\cdot\cos\theta} \cdot \frac{\sin\theta}{\sin\theta-\cos\theta}$
Now we can cancel out leaving $A = \frac{1}{\cos\theta} = \sec\theta$
