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Формулы тригонометрии

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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?=2sin1/2(?+?)cos1/2(?-?); sin?-sin?=2cos1/2(?+?)sin 1/2(?-?)

cos?+cos?=2cos1/2(?+?)cos1/2(?-?); cos?-cos?=-2sin1/2(?+?)sin 1/2(?-?)

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

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

sin??–sin??=cos??–cos??=sin(?+?)sin(?-?)

cos??–sin??=cos??–sin??=cos(?+?)cos(?-?)

sin?·sin?=1/2[cos(?-?)–cos(?+?)]; cos?·cos?=1/2[cos(?-?)+cos(?+?)]

sin?·cos?=1/2[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?)

sin1/2?=((((1–cos?)/2); sin?=(2tg1/2?)/(1+tg? 1/2?)

sin2?=2 sin?·cos?; sin3?=3sin?–4sin??

sin??=1/2(1–cos2?); sin??=(3 sin? – sin 3?) / 4

cos1/2?=(([(1+cos?)/2]; cos?=(1–tg? 1/2?)/(1+tg? 1/2?)

cos2?=cos??–sin??=1–2 sin??=2cos??–1; cos3?=4cos??–3 cos?

cos??=1/2(1+cos2?);cos??=(3cos?+cos3?)/4

tg1/2?=sin?/(1+cos?)=(1–cos?)/sin?= ((((1–cos?)/(1+cos?))

tg?=(2tg1/2?)/(1–tg? 1/2?); tg2?=(2tg?)/(1–tg??)=2/(ctg?–tg?)

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

ctg1/2?=sin?/(1–cos?)=(1+cos?)/sin?=((((1+cos?)/(1–cos?))

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

ctg3?=(3ctg?–ctg??)/(1–3 ctg??)

tg(1/4п+?)=(sin?+cos?)/(sin?–cos?); tg(1/4п–?)=(sin?–cos?)/(sin?+cos?)

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