№3. Упростите выражение: a) sin($$\frac{3\pi}{2}$$ - α) - cos(π + α); б) tg(π + α) + ctg($$\frac{\pi}{2}$$ - α); в) sin2α + (sinα - cosα)²; г) $$\frac{cosa}{1-sina}$$ - $$\frac{cosa}{1+sina}$$.

a) sin($$\frac{3\pi}{2}$$ - α) - cos(π + α) = -cos(α) - (-cos(α)) = -cos(α) + cos(α) = 0. б) tg(π + α) + ctg($$\frac{\pi}{2}$$ - α) = tg(α) + tg(α) = 2tg(α). в) sin2α + (sinα - cosα)² = sin2α + sin²α - 2sinαcosα + cos²α = sin2α - sin2α + sin²α + cos²α = 1. г) $$\frac{cosa}{1-sina}$$ - $$\frac{cosa}{1+sina}$$ = $$\frac{cos(a)(1 + sin(a)) - cos(a)(1 - sin(a))}{(1 - sin(a))(1 + sin(a))}$$ = $$\frac{cos(a) + cos(a)sin(a) - cos(a) + cos(a)sin(a)}{1 - sin^2(a)}$$ = $$\frac{2cos(a)sin(a)}{cos^2(a)}$$ = $$\frac{2sin(a)}{cos(a)}$$ = 2tg(a). Ответ: a) 0; б) 2tg(α); в) 1; г) 2tg(a)