Solve each equation in x over the interval [0, 2π) and each equation in θ over the interval [0°, 360°). Give exact solutions.
cos 2x + cos x = 0

Write each expression as a product of trigonometric functions. See Example 8.

sin 9x - sin 3x

Verify that each equation is an identity.

cos x = (1 - tan² (x/2))/(1 + tan² (x/2))

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth of a degree, as appropriate.

sin 2θ = cos 2θ +1

Solve each equation in x over the interval [0, 2π) and each equation in θ over the interval [0°, 360°). Give exact solutions.

sin x = sin 2x

Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.

2 sin θ = 2 cos 2θ

Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.

1 - sin x = cos 2x

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

d. sin 2α

sin α = 3/5, 0 < α < 𝝅/2, and sin β = 12/13, 𝝅/2 < β < 𝝅.

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

d. sin 2α

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