已知sin(α+β)=2⼀3,sin(α-β)=1⼀5,求sin2αsin2β的值

2025-05-05 01:33:49
推荐回答(2个)
回答1:

sin(α+β) = sinαcosβ+cosαsinβ = 2/3 ...... (1)

sin(α-β) = sinαcosβ-cosαsinβ = 1/5 ...... (2)

(1)+(2)得:2sinαcosβ = (2/3+1/5)
(1)-(2)得:2cosαsinβ = (2/3-1/5)

sin2αsin2β = 2sinαcosα * 2sinβcosβ = 2sinαcosβ * 2cosαsinβ = (2/3+1/5)(2/3-1/5) = 91/225

回答2:

展开算,然后加减