Тригонометрические формулы. Профильный ЕГЭ, часть 2


sin alpha +sin beta =2sin displaystyle  frac{alpha +beta }{2}cos displaystyle frac{alpha -beta }{2}

sin alpha -sin beta =2sindisplaystyle  frac{alpha -beta }{2}cos displaystyle frac{alpha +beta }{2}

cos alpha +cos beta =2cos displaystyle  frac{alpha +beta }{2}cos displaystyle frac{alpha -beta }{2}

cos alpha -cos beta =2sin  displaystyle  frac{alpha +beta }{2}sin  displaystyle frac{beta-alpha }{2}

2cosalpha  cos beta =cos (alpha +beta )+cos (alpha -beta )
2sin alpha  sin  beta =cos (alpha -beta )+cos (alpha+beta )
2sin alpha   cos beta =sin (alpha +beta )+sin (alpha -beta )

textup{tg}(alpha +beta )=displaystyle frac{textup{tg}alpha +textup{tg}beta }{1-textup{tg}alphacdot textup  {tg}beta }

textup{tg}(alpha -beta )=displaystyle frac{textup{tg}alpha -textup{tg}beta }{1+textup{tg}alphacdot textup  {tg}beta }

textup{tg}2alpha =displaystyle frac{2textup{tg}alpha  }{1-textup{tg}^{2}alpha }

sin 3alpha =3sin alpha -4sin ^{3}alpha
cos 3alpha =4cos ^{3}alpha -3cos alpha

sin alpha =displaystyle frac{2textup{tg}frac{alpha }{2}}{1+textup{tg}^{2}frac{alpha }{2}}

cos alpha =displaystyle frac{1-textup{tg}^{2}frac{alpha }{2}}{1+textup{tg}^{2}frac{alpha }{2}}

Ссылка на основную публикацию