Реферат: Формулы тригонометрии

tg(α+β)=(tgα+tgβ)/(1–tgα·tgβ); tg(α-β)=(tgα–tgβ)/(1+tgα·tgβ)

ctg(α+β)=(ctgα·ctgβ–1)/(ctgβ+ctgα); ctg(α+β)=(ctgα·ctgβ+1)/(ctgβ–ctgα)

sinα+sinβ=2sinЅ(α+β)cosЅ(α-β); sinα-sinβ=2cosЅ(α+β)sin Ѕ(α-β)

cosα+cosβ=2cosЅ(α+β)cosЅ(α-β); cosα-cosβ=-2sinЅ(α+β)sin Ѕ(α-β)

a·sinx+b·cosx=(aІ+bІ)sin(x+β), где tgβ=b/a

tgα  tgβ=sin(α+β)/(cosα·cosβ); ctgα  ctgβ=sin(βα)/(sinα·sinβ)

sinІα–sinІβ=cosІβ–cosІα=sin(α+β)sin(α-β)

cosІα–sinІβ=cosІβ–sinІα=cos(α+β)cos(α-β)

sinα·sinβ=Ѕ[cos(α-β)–cos(α+β)]; cosα·cosβ=Ѕ[cos(α-β)+cos(α+β)]

sinα·cosβ=Ѕ[sin(α+β)+sin(α-β)]

tgα·tgβ=(tgα+tgβ)/(ctgα+ctgβ)=-(tgα–tgβ)/(ctgα–ctgβ)

ctgα·tgβ=(ctgα+tgβ)/(tgα+ctgβ)=-(ctgα–tgβ)/(tgα–ctgβ)

ctgα·ctgβ=(ctgα+ctgβ)/(tgα+tgβ)=-(ctgα–ctgβ)/(tgα–tgβ)

sinЅα=((1–cosα)/2); sinα=(2tgЅα)/(1+tgІ Ѕα)

sin2α=2 sinα·cosα; sin3α=3sinα–4sinіα

sinІα=Ѕ(1–cos2α); sinіα=(3 sinα – sin 3α) / 4

cosЅα=[(1+cosα)/2]; cosα=(1–tgІ Ѕα)/(1+tgІ Ѕα)

cos2α=cosІα–sinІα=1–2 sinІα=2cosІα–1; cos3α=4cosіα–3 cosα

cosІα=Ѕ(1+cos2α);cosіα=(3cosα+cos3α)/4

tgЅα=sinα/(1+cosα)=(1–cosα)/sinα= ((1–cosα)/(1+cosα))

tgα=(2tgЅα)/(1–tgІ Ѕα); tg2α=(2tgα)/(1–tgІα)=2/(ctgα–tgα)

tg3α=(3tgα–tgіα)/(1–3tgІα)=tgα·tg(π/3+α)·tg(π/3–α)

ctgЅα=sinα/(1–cosα)=(1+cosα)/sinα=((1+cosα)/(1–cosα))

ctgα=(ctgІ Ѕα–1)/2ctg Ѕα; ctg2α=(ctgІα–1)/2ctgα=Ѕ(ctgα–tgα)

ctg3α=(3ctgα–ctgіα)/(1–3 ctgІα)

tg(јп+α)=(sinα+cosα)/(sinα–cosα); tg(јп–α)=(sinα–cosα)/(sinα+cosα)