упростить: ((cosa-cos 3a+cos 5a-cos 7a)/(sina+sin 3a+sin 5a+sin 7a))*2ctga

Question

упростить:
((cosa-cos 3a+cos 5a-cos 7a)/(sina+sin 3a+sin 5a+sin 7a))*2ctga

Answer 1

((cosa - cos 3a+cos 5a - cos 7a)/(sina +sin 3a+sin 5a+sin 7a))*2ctga=
=(-2Sin4αSinα + 2Sin4α Sin3α)/(2Sin4αCosα + 2Sin4αCos3α) * 2Cosα/Sinα=
= 2Sin4α(Sin3α - Sinα)/2Sin4α(Cosα+ Cos3α) * 2Cosα/Sinα=
=(Sin3α - Sinα)/(Cosα+ Cos3α) * 2Cosα/Sinα= =2SinαCos2α/2Cos2αCosα*Cosα/Sinα = 1