\[e^{ix}=cos x + i*sin x\]
\[1. \hspace{0.2cm} sin(α \pm β) = sin α * cos β \pm cos α * sin β;\] \[2. \hspace{0.2cm} cos(α \pm β) = cos α cos β \mp sin α sin β;\] \[3. \hspace{0.2cm} tg(α \pm β) = \frac{tg α \pm tg β}{1 \mp tg α * tg β};\] \[4. \hspace{0.2cm} ctg(α \pm β) = \frac{-1 \pm ctg α * ctg β}{ctg α \pm ctg β};\]
\[1. \hspace{0.2cm} sin (2α) = 2 sin α * cos α;\] \[2. \hspace{0.2cm} cos (2α) = cos (2α) − sin (2α);\] \[3. \hspace{0.2cm} cos (2α) = 2 * cos (2α) − 1;\] \[4. \hspace{0.2cm} cos (2α) = 1 − 2 sin (2α);\] \[5. \hspace{0.2cm} tg (2α) = \frac{2 tg α}{1 − tg (2α)};\] \[6. \hspace{0.2cm} ctg (2α) = \frac{ctg (2α) − 1}{2 ctg α};\]
\[1. \hspace{0.2cm} sin^2 \frac{α}{2} = \frac{1-cos α}{2};\] \[2. \hspace{0.2cm} cos^2 \frac{α}{2} = \frac{1+cos α}{2};\] \[3. \hspace{0.2cm} tg^2 \frac{α}{2} = \frac{1- cos α}{1+cos α};\] \[4. \hspace{0.2cm} ctg^2 \frac{α}{2} = \frac{1+cos α}{1-cos a};\]
\[1. \hspace{0.2cm} sin^2 α = \frac{1-cos α}{2};\] \[2. \hspace{0.2cm} cos^2 α = \frac{1+cos α}{2};\] \[3. \hspace{0.2cm} sin^3 α = \frac{3sin α - sin (3α)}{4};\] \[4. \hspace{0.2cm} cos^3 α = \frac{3cos α + cos (3α)}{4};\]
\[1. \hspace{0.2cm} sin α + sin β = 2sin \frac{α+β}{2} * cos \frac{α-β}{2};\] \[2. \hspace{0.2cm} sin α - sin β = 2sin \frac{α-β}{2} * cos \frac{α+β}{2};\] \[3. \hspace{0.2cm} cos α + cos β = 2cos \frac{α+β}{2} * cos \frac{α-β}{2};\] \[4. \hspace{0.2cm} cos α - cos β = 2sin \frac{α+β}{2} * sin \frac{β-α}{2};\]
\[1. \hspace{0.2cm} sin α * sin β = \frac{1}{2} * (cos(α-β)-cos(α+β));\] \[2. \hspace{0.2cm} cos α * cos β = \frac{1}{2} * (cos(α-β)+cos(α+β));\] \[3. \hspace{0.2cm} sin α * cos β = \frac{1}{2} * (sin(α-β)+sin(α+β));\]