Question

1+ctg^2a=ctg^2a/cos^2a

Answer 1

$mathtt{1+ctg^2a=frac{ctg^2a}{cos^2a};~1+frac{cos^2a}{sin^2a}=ctg^2a:cos^2a;~}\\mathtt{frac{sin^2a}{sin^2a}+frac{cos^2a}{sin^2a}=frac{cos^2a}{sin^2a}*frac{1}{cos^2a};~frac{sin^2a+cos^2a}{sin^2a}=frac{1}{sin^2a};~frac{1}{sin^2a}=frac{1}{sin^2a}}$