Упростите : (sin4a+2sin2a)*ctg2a ------------------------------ (cosa+ cos3a)*cosa

Question

Упростите :

(sin4a+2sin2a)*ctg2a
------------------------------
(cosa+ cos3a)*cosa

Comments

Пожалуйста с объяснением!

Answer 1

(sin4α+2sin2α)·ctg2α/(cosα+cos3α)·cosα=
=(2sin2αcos2α+2sin2α)·ctg2α/(2cos[(α+3α)/2]·cos[(α-3α)/2]·cosα)=
=2sin2α·(cos2α+1)·(cos2α/sin2α)/(2cos2α·cos(-α)·cosα)=
=2cos2α·(cos²α-sin²α+cos²α+sin²α)/2cos2α·cos²α=
=2cos2α·2cos²α/2cos2α·cos²α=2;