6. Trigonometric Identities and More Equations

In Exercises 7–14, use the given information to find the exact value of each of the following:a. sin 2θ2sin θ = ﹣ -------- , θ lies in quadrant III.3

In Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression.2 sin 15° cos 15°

In Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression.cos² 105° - sin² 105°

In Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression.𝝅2 cos² ------ ﹣ 18

In Exercises 43–44, express each product as a sum or difference.sin 6x sin 4x

In Exercises 43–44, express each product as a sum or difference.sin 7x cos 3x

In Exercises 45–46, express each sum or difference as a product. If possible, find this product's exact value.sin 2x - sin 4x

In Exercises 47–54, use the figures to find the exact value of each trigonometric function.θ θ2 sin ------- cos -------2 2