Question 595185
<img src="http://latex.codecogs.com/gif.latex?\Large \frac{9-\tan(\theta)}{9\csc(\theta)-\sec(\theta)}" title="x" />


<img src="http://latex.codecogs.com/gif.latex?\Large \frac{9-\frac{\sin(\theta)}{\cos(\theta)}}{\frac{9}{\sin(\theta)}-\frac{1}{\cos(\theta)}}" title="x" />


<img src="http://latex.codecogs.com/gif.latex?\Large \frac{9\left(\sin(\theta)\cos(\theta)\right)-\left(\frac{\sin(\theta)}{\cos(\theta)}\right)\left(\sin(\theta)\cos(\theta)\right)}{\left(\frac{9}{\sin(\theta)}\right)\left(\sin(\theta)\cos(\theta)\right)-\left(\frac{1}{\cos(\theta)}\right)\left(\sin(\theta)\cos(\theta)\right)}" title="x" />


<img src="http://latex.codecogs.com/gif.latex?\Large \frac{9\sin(\theta)\cos(\theta)-\sin^2(\theta)}{9\cos(\theta)-\sin(\theta)}" title="x" />


<img src="http://latex.codecogs.com/gif.latex?\Large \frac{\sin(\theta)\left(9\cos(\theta)-\sin(\theta)\right)}{9\cos(\theta)-\sin(\theta)}" title="x" />


<img src="http://latex.codecogs.com/gif.latex?\Large \sin(\theta)" title="x" />


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So <img src="http://latex.codecogs.com/gif.latex?\Large \frac{9-\tan(\theta)}{9\csc(\theta)-\sec(\theta)} = \sin(\theta)" title="x" /> for all allowed domain values of <img src="http://latex.codecogs.com/gif.latex?\Large \theta" title="x" />