Формулы тригонометрии

Формулы тригонометрии

tg(?+?)=(tg?+tg?)/(1–tg?·tg?); tg(?-?)=(tg?–tg?)/(1+tg?·tg?)

ctg(?+?)=(ctg?·ctg?–1)/(ctg?+ctg?); ctg(?+?)=(ctg?·ctg?+1)/(ctg?–ctg?)

sin?+sin?=2sinЅ(?+?)cosЅ(?-?); sin?-sin?=2cosЅ(?+?)sin Ѕ(?-?)

cos?+cos?=2cosЅ(?+?)cosЅ(?-?); cos?-cos?=-2sinЅ(?+?)sin Ѕ(?-?)

a·sinx+b·cosx=((aІ+bІ)sin(x+?), где tg?=b/a

tg? ( tg?=sin(?+?)/(cos?·cos?); ctg? ( ctg?=sin(?(?)/(sin?·sin?)

sinІ?–sinІ?=cosІ?–cosІ?=sin(?+?)sin(?-?)

cosІ?–sinІ?=cosІ?–sinІ?=cos(?+?)cos(?-?)

sin?·sin?=Ѕ[cos(?-?)–cos(?+?)]; cos?·cos?=Ѕ[cos(?-?)+cos(?+?)]

sin?·cos?=Ѕ[sin(?+?)+sin(?-?)]

tg?·tg?=(tg?+tg?)/(ctg?+ctg?)=-(tg?–tg?)/(ctg?–ctg?)

ctg?·tg?=(ctg?+tg?)/(tg?+ctg?)=-(ctg?–tg?)/(tg?–ctg?)

ctg?·ctg?=(ctg?+ctg?)/(tg?+tg?)=-(ctg?–ctg?)/(tg?–tg?)

sinЅ?=((((1–cos?)/2); sin?=(2tgЅ?)/(1+tgІ Ѕ?)

sin2?=2 sin?·cos?; sin3?=3sin?–4sinі?

sinІ?=Ѕ(1–cos2?); sinі?=(3 sin? – sin 3?) / 4

cosЅ?=(([(1+cos?)/2]; cos?=(1–tgІ Ѕ?)/(1+tgІ Ѕ?)

cos2?=cosІ?–sinІ?=1–2 sinІ?=2cosІ?–1; cos3?=4cosі?–3 cos?

cosІ?=Ѕ(1+cos2?);cosі?=(3cos?+cos3?)/4

tgЅ?=sin?/(1+cos?)=(1–cos?)/sin?= ((((1–cos?)/(1+cos?))

tg?=(2tgЅ?)/(1–tgІ Ѕ?); tg2?=(2tg?)/(1–tgІ?)=2/(ctg?–tg?)

tg3?=(3tg?–tgі?)/(1–3tgІ?)=tg?·tg(?/3+?)·tg(?/3–?)

ctgЅ?=sin?/(1–cos?)=(1+cos?)/sin?=((((1+cos?)/(1–cos?))

ctg?=(ctgІ Ѕ?–1)/2ctg Ѕ?; ctg2?=(ctgІ?–1)/2ctg?=Ѕ(ctg?–tg?)

ctg3?=(3ctg?–ctgі?)/(1–3 ctgІ?)

tg(јп+?)=(sin?+cos?)/(sin?–cos?); tg(јп–?)=(sin?–cos?)/(sin?+cos?)