What is \frac{\sin \theta}{1-\cot \theta}+\frac{\cos \theta}{1-\tan \theta} (\theta\neq\pi/4) equal to?
- A. \sin \theta+\cos \theta ✓
- B. \sin \theta-\cos \theta
- C. \cos \theta-\sin \theta
- D. -(\sin \theta+\cos \theta)
Correct Answer: A. \sin \theta+\cos \theta
Explanation
Convert to sines and cosines: \frac{\sin^2\theta}{\sin\theta - \cos\theta} + \frac{\cos^2\theta}{\cos\theta - \sin\theta} = \frac{\sin^2\theta - \cos^2\theta}{\sin\theta - \cos\theta} = \sin\theta + \cos\theta.
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