← Back

Module 5 Study Guide: Trig Identities

Verification Strategies

  1. Work one side only
  2. Convert to sin/cos
  3. Factor, combine fractions, multiply by conjugate
  4. Use Pythagorean identities

Sum & Difference Formulas

cos(A±B) = cosAcosB ∓ sinAsinB
sin(A±B) = sinAcosB ± cosAsinB
tan(A±B) = (tanA ± tanB)/(1 ∓ tanAtanB)

Double-Angle Formulas

sin2θ = 2sinθcosθ
cos2θ = cos²θ−sin²θ = 2cos²θ−1 = 1−2sin²θ
tan2θ = 2tanθ/(1−tan²θ)

Power-Reducing

sin²θ = (1−cos2θ)/2    cos²θ = (1+cos2θ)/2

Half-Angle Formulas

sin(θ/2) = ±√[(1−cosθ)/2]
cos(θ/2) = ±√[(1+cosθ)/2]
tan(θ/2) = (1−cosθ)/sinθ = sinθ/(1+cosθ)

Product-to-Sum

cosAcosB = (1/2)[cos(A−B)+cos(A+B)]
sinAsinB = (1/2)[cos(A−B)−cos(A+B)]
sinAcosB = (1/2)[sin(A+B)+sin(A−B)]

Sum-to-Product

sinA+sinB = 2sin((A+B)/2)cos((A−B)/2)
cosA+cosB = 2cos((A+B)/2)cos((A−B)/2)