Q2. Establish the identity using the right triangle shown.

Background

Topic: Trigonometric Identities and Right Triangles

This question is testing your ability to use the properties of right triangles and trigonometric ratios (sine, cosine, tangent) to establish a mathematical identity. The triangle has sides labeled 1 (opposite), x (adjacent), and u (hypotenuse), with angle .

Key Terms and Formulas

• Sine:

• Cosine:

• Tangent:

• Pythagorean Theorem:

Step-by-Step Guidance

1. Identify the sides of the triangle relative to angle : the side labeled 1 is opposite, x is adjacent, and u is the hypotenuse.

2. Write the trigonometric ratios for using the triangle:

3. Recall the Pythagorean Theorem for this triangle: .

4. Use the trigonometric ratios and the Pythagorean Theorem to set up an identity. For example, you might relate to 1.

5. Substitute the expressions for and in terms of and into the identity you are trying to establish.

Try solving on your own before revealing the answer!