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Module 5: Trig Identities Quick Ref

Sum/Difference

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

Double-Angle

sin2θ=2sinθcosθ
cos2θ=cos²−sin²=2cos²−1=1−2sin²
tan2θ=2tan/(1−tan²)

Half-Angle

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

Power-Reducing

sin²θ=(1−cos2θ)/2
cos²θ=(1+cos2θ)/2

Product ↔ Sum

cosAcosB = ½[cos(A−B)+cos(A+B)]
sinAsinB = ½[cos(A−B)−cos(A+B)]
sinA+sinB = 2sin((A+B)/2)cos((A−B)/2)
cosA+cosB = 2cos((A+B)/2)cos((A−B)/2)