Question

tg^2a-sin^2a=tg^2a*sin^2a доказать тождество

Answer 1

sin^2 a/ cos^2 a  - sin^2 a /1 = sin^2 a / cos ^2 a   * sin^2 a /1;
(sin^2 a - sin^2a*cos^2a) / cos^2 a = sin^4 a / cos^2 a;
cos^2a ≠ 0;
 cosa ≠ 0;
a ≠ pi/2  + pi*k;
sin^2 a - sin^2a * cos^2 a= sin^4 a;
sin^2 a(1 - cos^2 a) = sin^4 a;
sin^2 a * sin^2 a  = sin^4a;
 sin^4 a = sin^4 a.

Answer 2

tg²a - sin²a = tg²a · sin²a

tg²a - sin²a = sin²a/cos²a - sin²a · (cos²a) = sin²a - sin²a · cos²a/cos²a = sin²a(1 - cos²a)/cos²a  = sin²a · sin²a/cos²a = tg²a · sin²a 

 tg²a · sin²a =  tg²a · sin²a