Докажите тождества (ctga+1)^2+(ctga+1)^2=2/sin^2a

Докажем тождество: 

(ctg a + 1)^2 + (ctg a + 1)^2 = 2/sin^2 a; 

2 * (ctg a + 1)^2  = 2/sin^2 a;  

2 * (ctg^2 a + 2 * ctg a * 1 + 1^2) = 2/sin^2 a; 

2 * (ctg^2 a + 2 * ctg a + 1) = 2/sin^2 a; 

2 * (ctg^2 a + 2 * ctg a + 1)/2 = 2/sin^2 a/2;  

ctg^2 a + 2 * ctg a + 1 = 1/sin^2 a;  

cos^2 a/sin^2 a + 2 * cos a/sin a + 1 = 1/sin^2 a; 

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

(sin a + cos a)^2/sin^ 2 = 1/sin^2 a; 

Тождество неверно.