Trigonometric Identities
Compound Angle Formulae
sin(A + B ) = sinA cosB + cosA sinB
sin(A − B ) = sinA cosB − cosA sinB
cos(A + B ) = cosA cosB − sinA sinB
cos(A − B ) = cosA cosB + sinA sinB
tanA + tanB
tan(A + B ) = 1−tanA tanB
tanA − tanB
tan(A − B ) = 1 + tanA tanB
Double Angle Formulae
sin2A = 2 sinA cosA
cos 2A = cos2 A − sin2 A
= 1 − sin2 A
= 2cos2 A − 1
2tan A
tan2A = 1−tan 2A
Alternative Forms
a sinθ + b cosθ = r sin(θ + α)
a sinθ − b cosθ = r sin(θ − α)
a cosθ + b sinθ = r cos(θ − α)
a cosθ − bsinθ = r cos(θ + α)
W here r = √a2 + b2 and tan α = b
a
Compound Angle Formulae
sin(A + B ) = sinA cosB + cosA sinB
sin(A − B ) = sinA cosB − cosA sinB
cos(A + B ) = cosA cosB − sinA sinB
cos(A − B ) = cosA cosB + sinA sinB
tanA + tanB
tan(A + B ) = 1−tanA tanB
tanA − tanB
tan(A − B ) = 1 + tanA tanB
Double Angle Formulae
sin2A = 2 sinA cosA
cos 2A = cos2 A − sin2 A
= 1 − sin2 A
= 2cos2 A − 1
2tan A
tan2A = 1−tan 2A
Alternative Forms
a sinθ + b cosθ = r sin(θ + α)
a sinθ − b cosθ = r sin(θ − α)
a cosθ + b sinθ = r cos(θ − α)
a cosθ − bsinθ = r cos(θ + α)
W here r = √a2 + b2 and tan α = b
a
