Uzasadnij tożsamość: a) tg[latex]tg^{2}alpha- sin^{2}alpha=tg^{2}alpha cdot sin^{2}alpha[/latex] b) [latex]cosalpha cdot ctgalpha + sinalpha =frac{1}{sinalpha}[/latex]

a) tg^2 a - sin^2 a = tg^2 a * sin^2 a    L = tg^2 a - sin^2 a =  sin^2 a/cos^2 a - sin^2 a =   (sin^2 a - sin^2 a cos^2 a)/cos^2a = sin^2 a(1 - cos^2 a)/cos^2 a =  sin^2 a/cos^2 a * sin^2 a =  tg^2 a * sin^2 a  L = P b) cos a * ctg a + sin a = 1/sin a    L = cos a * ctg a + sin a =  cos a * cos a/sin a + sin a =  (cos^2 a + sin^2 a)/sin a = 1/sin a  L = P