The coprocessor of the 8086 processor is the 8087 coprocessor. The 8087 is also known as the math coprocessor or the numeric data processor. It is specifically designed to perform mathematical operations and enhance the computational capabilities of the 8086 processor.

Below are the reasons why the 8087 coprocessor is the correct answer:

1. Enhanced mathematical capabilities:
- The 8087 coprocessor is specifically designed for handling mathematical operations efficiently.
- It provides hardware support for floating-point arithmetic, which is essential for complex mathematical calculations.
- With the 8087 coprocessor, the 8086 processor can offload complex mathematical computations and achieve faster and more accurate results.

2. Data processing efficiency:
- The 8087 coprocessor operates in parallel with the 8086 processor, allowing simultaneous execution of instructions.
- It can execute floating-point instructions independently, which reduces the burden on the main processor and improves overall system performance.
- The coprocessor's efficient data processing capabilities make it ideal for applications that involve scientific calculations, engineering simulations, financial analysis, and more.

3. Specific compatibility:
- The 8087 coprocessor is designed to work specifically with the 8086 processor.
- It utilizes a dedicated instruction set and communicates with the 8086 processor through a specialized bus interface.
- The coprocessor is physically connected to the 8086 processor via a socket, allowing for easy integration and compatibility.

4. Upgradability:
- The 8087 coprocessor can be added to a system that already has an 8086 processor, providing an upgrade path for enhanced mathematical capabilities.
- This upgradability allows users to improve the performance of their system without needing to replace the entire processor.

In conclusion, the 8087 coprocessor is the correct answer as it provides enhanced mathematical capabilities, efficient data processing, specific compatibility with the 8086 processor, and the ability to upgrade existing systems for improved performance.