1. Half-Angle Identities
5.4C

2. Half-Angle Identities
Sin 𝑥 2 = ± 1− cos 𝑥 2
Cos 𝑥 2 = ± cos 𝑥 2
Tan 𝑥 2 = ± 1− cos 𝑥 1+ cos 𝑥
Tan 𝑥 2 = 1− cos 𝑥 sin 𝑥
Tan 𝑥 2 = sin 𝑥 1+ cos 𝑥

3. Ex. Find the values between [0, 2𝜋] for which the following is true:
Cos2x = sin2( 𝑥 2 )
Cos2x = (1− cos 𝑥)
Cos2x = 1− cos 𝑥 2
2cos2x = 1 – cos x
2( 1+ cos 2𝑥 2 )=1− cos 𝑥
1 + cos 2x = 1 – cos x

4. cos 2x + cos x = 0 cos2x – sin2x + cos x = 0 cos2x + cos2x – 1 + cos x = 0 2cos2x – 1 + cos x = 0 2cos2x + cos x – 1 = 0 (2cos x – 1)(cos x + 1) = 0 2cos x – 1 = 0 cos x + 1 = 0 2cos x = 1 cos x = -1 Cos x = 1 2 x = 180° x = 60°