# Worksheet: Proving Trigonometric Identities

In this worksheet, we will practice deriving the Pythagorean identity and solving proofs problems related to it.

**Q1: **

The figure shows a unit circle and a radius with the lengths of its - and -components. Use the Pythagorean theorem to derive an identity connecting the lengths 1, , and .

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**Q2: **

Consider the identity . We can use this to derive two new identities.

First, divide both sides of the identity by to find an identity in terms of and .

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Now, divide both sides of the identity through by to find an identity in terms of and .

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**Q3: **

The lengths of the sides of the right triangle shown in the figure are 3, 4, and 5. Find the areas of the squares on the three sides, and find a relationship between them.

- A area of the square on the hypotenuse (25) sum of the areas of the squares on the legs
- B area of the square on the hypotenuse (25) > sum of the areas of the squares on the legs
- C area of the square on the hypotenuse (25) < sum of the areas of the squares on the legs
- D area of the square on the hypotenuse (25) = sum of the areas of the squares on the legs