Question

$(1+ctg ^{2} a)(1-sin ^{2} a)$

Answer 1

$(1 + text{ctg}^2 a)(1 - sin^2 a) = (1 + frac{cos^2 a}{sin^2 a})(1 - sin^2 a) = \\ = 1 + frac{cos^2 a}{sin^2 a} - sin^2a - frac{cos^2 a}{sin^2 a}sin^2 a = \\ = cos^2 a + sin^2 a + frac{cos^2 a}{sin^2 a} - sin^2a - cos^2a = frac{cos^2a}{sin^2 a} = boxed{text{ctg}^2 a}$