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?=2sin½(?+?)cos½(?-?); sin?-sin?=2cos½(?+?)sin ½(?-?)
cos?+cos?=2cos½(?+?)cos½(?-?); cos?-cos?=-2sin½(?+?)sin ½(?-?)
a·sinx+b·cosx=?(a²+b²)sin(x+?), где tg?=b/a
tg? ? tg?=sin(?+?)/(cos?·cos?); ctg? ? ctg?=sin(???)/(sin?·sin?)
sin²?–sin²?=cos²?–cos²?=sin(?+?)sin(?-?)
cos²?–sin²?=cos²?–sin²?=cos(?+?)cos(?-?)
sin?·sin?=½[cos(?-?)–cos(?+?)]; cos?·cos?=½[cos(?-?)+cos(?+?)]
sin?·cos?=½[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?)
sin½?=??((1–cos?)/2); sin?=(2tg½?)/(1+tg² ½?)
sin2?=2 sin?·cos?; sin3?=3sin?–4sin³?
sin²?=½(1–cos2?); sin³?=(3 sin? – sin 3?) / 4
cos½?=??[(1+cos?)/2]; cos?=(1–tg² ½?)/(1+tg² ½?)
cos2?=cos²?–sin²?=1–2 sin²?=2cos²?–1; cos3?=4cos³?–3 cos?
cos²?=½(1+cos2?);cos³?=(3cos?+cos3?)/4
tg½?=sin?/(1+cos?)=(1–cos?)/sin?= ??((1–cos?)/(1+cos?))
tg?=(2tg½?)/(1–tg² ½?); tg2?=(2tg?)/(1–tg²?)=2/(ctg?–tg?)
tg3?=(3tg?–tg³?)/(1–3tg²?)=tg?·tg(?/3+?)·tg(?/3–?)
ctg½?=sin?/(1–cos?)=(1+cos?)/sin?=??((1+cos?)/(1–cos?))
ctg?=(ctg² ½?–1)/2ctg ½?; ctg2?=(ctg²?–1)/2ctg?=½(ctg?–tg?)
ctg3?=(3ctg?–ctg³?)/(1–3 ctg²?)
tg(¼п+?)=(sin?+cos?)/(sin?–cos?); tg(¼п–?)=(sin?–cos?)/(sin?+cos?)