[latex](1+ctg ^{2} a)(1-sin ^{2} a)[/latex]

[latex](1 + \text{ctg}^2 a)(1 - \sin^2 a) = (1 + \frac{\cos^2 a}{\sin^2 a})(1 - \sin^2 a) = \\\\ = 1 + \frac{\cos^2 a}{\sin^2 a} - \sin^2a - \frac{\cos^2 a}{\sin^2 a}\sin^2 a = \\\\ = \cos^2 a + \sin^2 a + \frac{\cos^2 a}{\sin^2 a} - \sin^2a - \cos^2a = \frac{\cos^2a}{\sin^2 a} = \boxed{\text{ctg}^2 a} [/latex]