Обоснуйте тождество 2sin^2()/tg2*tg=cos^2()-sin^2()

Докажем тождество:

2 * sin^2 a/(tg (2 * a) * tg ) = cos^2 - sin^2 ;  

2 * sin^2 a/(tg (2 * a) * sin /cos a) = cos^2 - sin^2 ;  

2 * sin^2 a/((tg (2 * a) * sin )/cos a) = cos^2 - sin^2 ;  

2 * sin^2 a * cos a/(tg (2 * a) * sin a) = cos^2 a - sin^2 a; 

2 * sin a * cos a/(tg (2 * a) * 1) = cos^2 a - sin^2 a;  

2 * sin a * cos a/(sin (2 * a)/cos (2 * a)) = cos^2 a - sin^2 a;  

sin (2 * a)/((sin (2 * a)/cos (2 * a)) = cos^2 a - sin^2 a;  

sin (2 * a) * cos (2 * a)/sin (2 * a) = cos^2 a - sin^2 a; 

cos (2 * a) = cos^2 a - sin^2 a; 

cos^2 a - sin^2 a = cos^2 a - sin^2 a; 

Тождество правильно.