Упростите выражение: a) sin(π + α) + cos(3π/2 - α); б) tg(π/2 + α) - ctg(2π - α); в) (cos 2α + 2sin²(π – α)) / (sina/(1+cosa) + sina/(1-cosa))

a) sin(π + α) + cos(3π/2 - α) = -sin α + sin α = 0

б) tg(π/2 + α) - ctg(2π - α) = -ctg α + ctg α = 0

в) (cos 2α + 2sin²(π – α)) / (sina/(1+cosa) + sina/(1-cosa)) = (cos 2α + 2sin²α) / (sina(1-cosa + 1+cosa) / (1-cos²a)) = (cos 2α + 2sin²α) / (2sina/sin²a) = (cos 2α + 2sin²α) / (2/sina) = ((cos²α - sin²α) + 2sin²α) * (sina/2) = (cos²α + sin²α) * (sina/2) = 1 * (sina/2) = sina/2

Ответ: a) 0; б) 0; в) sinα/2