http://www.purplemath.com/modules/idents.htm

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sin(A+B)

sinAcosB+cosAsinB

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sin(A-B)

sinAcosB-cosAsinB

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cos(A+B)

cosAcosB-sinAsinB

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cos(A-B)

cosAcosB+sinAsinB

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tan(A+B)

(tanA+tanB)/(1-tanAtanB)

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tan(A-B)

(tanA-tanB)/(1+tanAtanB)

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cos2A (in terms of both sin and cos)

cos²A-sin²A

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tan(A/2) (in terms of cos only)

±√((1-cosA)/(1+cosA))

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tan(A/2) (rationalized)

(1-cosA)/sinA and sinA/(1+cosA)

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sinA + sinB

2sin((A+B)/2)cos((A-B)/2)

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sinA-sinB

2cos((A+B)/2)sin((A-B)/2)

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cosA+cosB

2cos((A+B)/2)cos((A-B)/2)

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cosA-cosB

-2sin((A+B)/2)sin((A-B)/2)

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sinAcosB

(1/2)(sin(A+B)+sin(A-B))

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cosAcosB

(1/2)(cos(X-Y)+cos(X+Y))

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sinAsinB

(1/2)(cos(X-Y)-cos(X+Y))