cos^2a+tg^2a+sin^2a=tg^2a+1
сos^2a+tg^2a+sin^2a = cos^2a + sin^2a/cos^2a + sin^2a = (cos^4a+sin^2a+sin^2a*cos^2a)/ cos^2a = 1/cos^2a
tg^2a+1 = sin^2a/cos^2a + 1 = sin^2a+cos^2a/cos^2a = 1/cos^2a
1/cos^2a=1/cos^2 -> тождество доказано
cos^2a+tg^2a+sin^2a=tg^2a+1
сos^2a+tg^2a+sin^2a = cos^2a + sin^2a/cos^2a + sin^2a = (cos^4a+sin^2a+sin^2a*cos^2a)/ cos^2a = 1/cos^2a
tg^2a+1 = sin^2a/cos^2a + 1 = sin^2a+cos^2a/cos^2a = 1/cos^2a
1/cos^2a=1/cos^2 -> тождество доказано