Докажите тождество: (2tg^2a * cos^2a + 2cos^2a)* sina + 3sina = 5sina

Question

Докажите тождество:

(2tg^2a * cos^2a + 2cos^2a)* sina + 3sina = 5sina

Answer 1

(sin2a/cos2a)(sina/cosa)/((sin2a/cos2a)-(sina/cosa))= =(sin2asina/cos2acosa)/(sin2acosa-sinacos2a/cos2acosa)= =sin2asina/(sin2acosa-sinacos2a)=sina/(cosa-(sinacos2a/sin2a))= =sina/(cosa-(cos2a/2cosa))=2sinacosa/2cos.^2a-cos2a= =2sinacosa/2cos.^2-cos.^2+sin.^2=2sinacosa/cos.^2a+sin.^2a=2sinacosa=sin2a