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Uncommon sum-diff/double angle, power-reducing/half angle, StP, PtS

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(tan(a)+tan(b))/(1-tan(a)tan(b))

tan(a+b)

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(tan(a)-tan(b))/(1+tan(a)tan(b))

tan(a-b)

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2tan(a)/(1-tan²(a))

tan(2a)

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2sin((a+b)/2)cos((a-b)/2)

sin(a)+sin(b)

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2cos((a+b)/2)sin((a-b)/2)

sin(a)-sin(b)

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2cos((a+b)/2)cos((a-b)/2)

cos(a)+cos(b)

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-2sin((a+b)/2)sin((a-b)/2)

cos(a)-cos(b)

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(cos(a-b)-cos(a+b))/2

sin(a)sin(b)

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(cos(a-b)+cos(a+b))/2

cos(a)cos(b)

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(sin(a+b)+sin(a-b))/2

sin(a)cos(b)