Sections:

Trigonometric Identities and Equations, Page 18

Double-Angle and Half-Angle Identities

The last sets of identities that need to be discussed are the Double-Angle Identities and the Half-Angle Identities.

Double-Angle Identities

sin2θ = 2sinθ cosθ; cos2θ = (cosθ)^2 - (sinθ)^2; cos2θ = 2 (cosθ)^2 - 1; cos2θ = 1 - 2 (sinθ)^2; tan2θ = 2tanθ/(1 - (tanθ)^2)

Half-Angle Identities

sinα/2 = ± square root of [(1 - cosα)/2]; cosα/2 = ± square root of [(1 + cosα)/2]; tanα/2 = ± square root of [(1 - cosα)/(1 + cosα], cosα does not equal -1