Формулы сложения тригонометрических функций

1) Cos6αCos2α - Sin6αSin2α = Cos(6α + 2α) = Cos8α

2) Sin(- 15°)Cos75° + Cos15°Sin75° = Sin75°Cos15° - Sin15°Cos75° =

= Sin(75° - 15°) = Sin60° =√3/2

$\frac{Cos64^{o}Cos4^{o}+Sin64^{o}Sin4^{o}}{Sin19^{o}Cos41^{o}+Sin41^{o}Cos19^{o} } =\frac{Cos(64^{o}-4^{o})}{Sin(19^{o}+41^{o})}=\frac{Cos60^{o} }{Sin60^{o} } =Ctg60^{o}=\frac{\sqrt{3} }{3}$

4) Cos(α - β) - 2SinαSinβ = CosαCosβ + SinαSinβ - 2SinαSinβ =

= CosαCosβ - SinαSinβ = Cos(α + β)