Chapter 5

Ch 5.3 : The Double-Angle and Half-Angle Identities
Theorem (The Double-Angle Identities)
◮ cos(2α) = cos 2 α − sin 2 α = 1 − 2 sin 2 α = 2 cos 2 α − 1
◮ sin(2α) = 2 sin α cos α
◮ tan(2α) =
2 tan α
1−tan 2 α
Let’s verify these identities.