Question

15 балов- 1 пример
Доказать тождество
(sin2α-sin3α+sin4α) / (cos2α-cos3α+cos4α)=tg3α

Answer 1

$frac{ sin(2alpha)- sin(3alpha)+ sin(4alpha)}{ cos(2alpha)- cos(3alpha)+ cos(4alpha)}= frac{ sin(2alpha)+ sin(4alpha)- sin(3alpha)}{ cos(2alpha)+ cos(4alpha)- cos(3alpha)}=$

$=frac{ 2sin(3alpha)*cos(2alpha)- sin(3alpha)}{ 2cos(3alpha)*cos(2alpha)- cos(3alpha)}= frac{ sin(3alpha)*[2cos(2alpha)- 1]}{ cos(3alpha)*[2cos(2alpha)-1]}= frac{sin(3alpha)}{cos(3alpha)} =tg(3 alpha )$