Упростите выражение: a) sin(π + a) + cos($$\frac{3π}{2}$$-a); б) tg ($$\frac{π}{2}$$ + a) - ctg(2π – α); в) cos 2a + 2 sin²(π – α) г) $$\frac{sin α}{1+cos α}$$ + $$\frac{sin α}{1-cos α}$$.

a) sin(π + a) + cos($$\frac{3π}{2}$$-a) sin(π + a) = -sin(a) cos($$\frac{3π}{2}$$-a) = -sin(a) -sin(a) - sin(a) = -2sin(a) Ответ: -2sin(a) б) tg ($$\frac{π}{2}$$ + a) - ctg(2π – α) tg ($$\frac{π}{2}$$ + a) = -ctg(a) ctg(2π – α) = ctg(-α) = -ctg(α) -ctg(a) - (-ctg(a)) = -ctg(a) + ctg(a) = 0 Ответ: 0 в) cos 2a + 2 sin²(π – α) sin(π – α) = sin(α) 2sin²(π – α) = 2sin²(α) cos 2a + 2 sin²(α) = cos²(α) - sin²(α) + 2sin²(α) = cos²(α) + sin²(α) = 1 Ответ: 1 г) $$\frac{sin α}{1+cos α}$$ + $$\frac{sin α}{1-cos α}$$ $$\frac{sin α}{1+cos α}$$ + $$\frac{sin α}{1-cos α}$$ = $$\frac{sin α(1-cos α) + sin α(1+cos α)}{(1+cos α)(1-cos α)}$$ = $$\frac{sin α - sin α cos α + sin α + sin α cos α}{1 - cos^2 α}$$ = $$\frac{2sin α}{sin^2 α}$$ = $$\frac{2}{sin α}$$ Ответ: $$\frac{2}{sin α}$$