Доказать тождество 1 + ctg2a = 1 / sin2a

[latex]1+ctg^2a= \frac{1}{sin^2a} \\ 1+ \frac{cos^2a}{sin^2a}=\frac{1}{sin^2a} \\ \frac{sin^2a+cos^2a}{sin^2a}=\frac{1}{sin^2a} \\ \frac{1}{sin^2a}=\frac{1}{sin^2a} [/latex]

1+ctg2a=1/sin2a 1+cos2a/sin2a=1/sin2a (sin2a+cos2a)/sin2a=1/sin2a 1/sin2a=1/sin2a (т.к. sin2a+cos2a=1)