Introduction:
When it comes to preparing for the Mathematics Optional subject for UPSC, revising the concepts of geometry and trigonometry is crucial. However, whether to revise these concepts separately or together depends on various factors. Let us delve into the details to understand the advantages of both approaches.

Revising Geometry and Trigonometry Separately:
1. Focus: When revising geometry and trigonometry separately, you can dedicate focused time to each subject. This allows you to delve deep into the concepts, understand them thoroughly, and strengthen your foundation in both areas.
2. Clarity: Separating the revision of geometry and trigonometry helps in better conceptual clarity. It prevents confusion between the two subjects and allows you to grasp the nuances of each independently.
3. Practice: By revising separately, you can practice a sufficient number of problems from each subject. This enhances your problem-solving skills and helps you gain confidence in tackling questions from both geometry and trigonometry.

Revising Geometry and Trigonometry Together:
1. Interconnectedness: Geometry and trigonometry are closely related subjects. Many concepts in geometry require the application of trigonometry, and vice versa. Therefore, revising them together can help you understand the interconnections between the two subjects and strengthen your overall understanding.
2. Efficiency: If you are short on time, revising geometry and trigonometry together can be more efficient. It allows you to cover a broader range of topics simultaneously, making your revision more comprehensive.
3. Application: Many real-life problems involve the application of both geometry and trigonometry. By revising them together, you develop a holistic approach to problem-solving, which can be advantageous in the UPSC examination.

Conclusion:
Both revising geometry and trigonometry separately and together have their own advantages. It ultimately depends on your personal preferences, time availability, and learning style. If you have ample time, revising them separately can provide a more detailed and focused understanding. On the other hand, if time is a constraint and you want to grasp the interconnectedness of the two subjects, revising them together might be a better option. Therefore, choose the approach that suits you best and aligns with your preparation strategy.