1-cos2x / 1+cos2x = tg²x Докажите тождество

Докажем тождество:

(1 - cos (2 * x))/(1 + cos (2 * x)) = tg^2 x; 

(sin^2 x + cos^2 x - cos (2 * x))/(sin62 x + cos^2 x + cos (2 * x)) = tg^2 x; 

(sin^2 x + cos^2 x - (cos^2 x - sin^2 x))/(sin62 x + cos^2 x + cos^2 x - sin^2 x) = tg^2 x;  

(sin^2 x + cos^2 x - cos^2 x + sin^2 x))/(sin^2 x + cos^2 x + cos^2 x - sin^2 x) = tg^2 x;  

Приведем подобные значения.  

(sin^2 x + 0 + sin^2 x))/(0 + cos^2 x + cos^2 x) = tg^2 x;   

(sin^2 x + sin^2 x))/(cos^2 x + cos^2 x) = tg^2 x;   

2 * sin^2 x/(2 * cos^2 x) = tg^2 x; 

sin62 x/cos^2 x = tg^2 x; 

tg^2 x = tg^2 x; 

Тождество верно.