Question

第7题求教。

Answer 1

所求＝sinA^2 + sinB^2 + 2sinAsinB + cosA^2 + cosB^2 + 2cosAcosB
＝2 + 2(cos(A-B))
= 2 + 2/3
=8/3

追问

谢

Answer 2

sin(α+β)=2/3
sin(α-β)=1/5
To find: tanα/tanβ

solution
sin(α+β)=2/3
sinα.cosβ+cosα.sinβ =2/3 (1)

sin(α-β)=1/5
sinα.cosβ-cosα.sinβ =1/5 (2)
(1)+(2)
sinα.cosβ = 6/15 (3)

(1)-(2)
cosα.sinβ =4/15 (4)

(3)/(4)
tanα/tanβ = 3/2

追问

第四题

追答

(4)
[2(cos30°+isin30°)]^5
=2^5.(cos150°+isin150°)
=32(-√3/2 + (1/2) i)

=