# Tangent of a Difference: Trig Identity Puzzle + Proof!

- Author:
- Tim Brzezinski

Carefully observe the diagram below. Notice .
Slide the black slider slowly and

**CAREFULLY OBSERVE THE DYNAMICS THAT TAKE PLACE.**After doing so, answer the questions and complete the activity prompts that appear below this applet.## Note: AE = 1.

## 1.

What can we conclude about and ? Why can we conclude this?

## 2.

Given your response to (1), write an equation that expresses the relationship among the lengths *AF*, *AB*, *CD*, and *DB*.

## 3.

The 4 text boxes (containing trigonometric expressions) that appeared at the end of these dynamics represent the lengths of the 4 BOLD SEGMENTS you see in this diagram. Drag each expression next to its appropriate segment in this diagram.

## 4.

Use your results from (3) and (2) to write an expression for in terms of these expressions (within the given diagram). What do you get?