https://file.aiquickdraw.com/mathbot/file/17295830407882gge8w65.jpg

From the image, it looks like the equation given is:

\[ \text{If } \tan y = 1 \text{ then } \tan y = a - b. \]

This is suggesting that \( \tan y = 1 \) implies something about the values \( a \) and \( b \). Let's break this down step by step:

1. **Step 1: Analyze \( \tan y = 1 \)**
   - The equation \( \tan y = 1 \) implies that the angle \( y \) corresponds to a value where the tangent of the angle is equal to 1.
   - This happens at angles where \( y = \frac{\pi}{4} + n\pi \) (in radians) or \( y = 45^\circ + n \times 180^\circ \) (in degrees), where \( n \) is an integer.

2. **Step 2: Interpret the relation \( \tan y = a - b \)**
   - If \( \tan y = a - b \), we can substitute the value of \( \tan y = 1 \) into this equation. Thus:
     \[
     1 = a - b
     \]
   - This equation tells us that \( a - b = 1 \). 

### Conclusion
- If \( \tan y = 1 \), then \( a - b = 1 \). This is a simple linear equation that relates \( a \) and \( b \).

Would you like to explore this further or go into more details on any particular step?

Here are 5 questions to extend this topic:
1. How can we solve \( a - b = 1 \) if we have additional conditions for \( a \) or \( b \)?
2. What are the general solutions to \( \tan y = 1 \) in radians and degrees?
3. Can \( a - b = 1 \) be applied in a trigonometric identity scenario?
4. How does the behavior of the tangent function differ from sine and cosine?
5. What is the periodicity of the tangent function and how does that affect solutions to trigonometric equations?

**Tip:** When solving trigonometric equations like \( \tan y = 1 \), remember that tangent is periodic with a period of \( \pi \) radians (or 180 degrees).

Learn how to solve the trigonometric equation where tan(y) = 1 then tan(y) = a - b. This problem involves key concepts in trigonometry, including the properties of the tangent function. Suitable for students in Grades 11-12.

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