Double and Half Angle Identities

Question 1

sin(2θ)

Answer 1

2sin(θ)cos(θ)

Question 2

cos(2θ)

Hint: there are 3

Answer 2

2cos^2(θ) – 1

cos^2(θ) – sin^2(θ)

1 – sin^2(θ)

Question 3

tan(2θ)

Answer 3

2tan(θ) OVER 1 – tan^2(θ)

Question 4

sin(θ/2)

Answer 4

+ or – square root of (1 – cos(θ) OVER two)

Question 5

cos(θ/2)

Answer 5

+ or – square root of (1 + cos(θ) OVER two)

Question 6

tan(θ/2)

Answer 6

sinθ OVER 1 + cosθ