Simplify the expression: $\frac{\sin \theta - \cos \theta + 1}{\sin \theta + \cos \theta - 1}$.
Options:
- A: $\sec \theta - \tan \theta$
- B: $\sec \theta + \tan \theta$
- C: $\csc \theta + \cot \theta$
- D: $\csc \theta - \cot \theta$
Related Practice Questions:
- 3 men or 4 women or 6 boys can complete a work in 25 days. How many days will it take for 2 men, 3 women, and 2 boys working together to complete the same work?
- A and B together can complete a piece of work in 15 days, while B alone can complete it in 20 days. Both start working together, but A leaves after 5 days. In how many additional days will B complete the remaining work?
- A can complete a work in 12 days, and B can complete it in 18 days. If they work on alternate days starting with A, in how many days will the work be completed?
- Why is copper considered highly pure and extensively used in religious rituals by Hindus today according to the historical context of natural resources?
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