Докажите тождество: sin 2a - tg a = cos 2a tg a

Question

Докажите тождество:

sin 2a - tg a = cos 2a tg a

Answer 1

sin^2 a * tg a - cos^2 a=
= sin^3 a / cos a - 1+ sin^2 a =
= sin^3 a / sqrt(1-sin^2 a) - 1+ sin^2 a =
= 1/27 / sqrt(1-1/9) -1 + 1/9 = 
= 1/(9sqrt(8) -8/9 = 
= (sqrt(2)-32)/36