###
tan 2x

(2 tan x) / (1 - tan²x)

###
sin (x + y)

sin x cos y + sin y cos x

###
sin (x - y)

sin x cos y - sin y cos x

###
cos (x + y)

cos x cos y - sin x sin y

###
cos (x - y)

cos x cos y + sin x sin y

###
tan (x + y)

(tan x + tan y) / (1 - tan x tan y)

###
tan (x - y)

(tan x - tan y) / (1 + tan x tan y)

###
tan²x

(1 - cos 2x) / (1 + cos 2x)

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