Найдите sin 2а, если cosa = -√5/√8, αε(π/2; π).

Given cos α = -√5/√8 and α is in the second quadrant (π/2 < α < π), sin α will be positive. We use the identity sin²α + cos²α = 1. So, sin²α = 1 - (-√5/√8)² = 1 - 5/8 = 3/8. Thus, sin α = √(3/8) = √3 / (2√2) = √6 / 4. Now, we use the double angle formula: sin 2α = 2 sin α cos α = 2 * (√6 / 4) * (-√5 / √8) = 2 * (√6 / 4) * (-√5 / (2√2)) = -2√30 / (8√2) = -√15 / (4√2) = -√30 / 8.