In Exercises 39–42, use double- and half-angle formulas to find the exact value of each expression. sin 22.5°

Solve each equation over the interval [0, 2π). Write solutions as exact values or to four decimal places, as appropriate.

sin x/2 - cos x/2 = 0

Solve each equation over the interval [0, 2π). Write solutions as exact values or to four decimal places, as appropriate

tan 2x + sec 2x = 3

In Exercises 35–38, find the exact value of the following under the given conditions:

e. cos( β/2)

sin α = -1/3, 𝝅 < α < 3𝝅/2, and cos β = -1/3, 𝝅 < β < 3𝝅/2.

In Exercises 39–46, use a half-angle formula to find the exact value of each expression. cos 22.5°

In Exercises 39–46, use a half-angle formula to find the exact value of each expression. sin 105°

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