Confirming a Double-Angle Identity (7.6.1)

Question 1

• The double-angle identities arise from the sum identities (from the sum and difference identities) when the two angles being added are equal. It is important to remember that one side of the identity refers to double angles while the other side refers to single angles. This shift can be very useful in solving problems.

Answer 1

• The double-angle identities arise from the sum identities (from the sum and difference identities) when the two angles being added are equal. It is important to remember that one side of the identity refers to double angles while the other side refers to single angles. This shift can be very useful in solving problems.

Question 2

• The double-angle identities:
  
  • sin 2θ = 2 sinθ cosθ
  • cos 2θ = cos2θ – sin2θ
  • cos 2θ = 1 – 2sin2θ
  • cos 2θ = 2cos2θ – 1
  • tan 2θ = (2tanθ)/1-tan^2θ

Answer 2

• The double-angle identities:
  
  • sin 2θ = 2 sinθ cosθ
  • cos 2θ = cos2θ – sin2θ
  • cos 2θ = 1 – 2sin2θ
  • cos 2θ = 2cos2θ – 1
  • tan 2θ = (2tanθ)/1-tan^2θ