Question

求2.4题怎么做

Answer 1

2(1)sin(α+β)=sinαcosβ + cosαsinβ=1/2①
sin(α-β)=sinαcosβ - cosαsinβ=1/3②
①+②得：2sinαcosβ=5/6
①-②得：2cosαsinβ=1/6
∵2sinαcosβ=5•(1/6)
∴2sinαcosβ=5•2cosαsinβ
即：sinαcosβ=5cosαsinβ
(2)根据(1)，两边同除以cosαcosβ
sinαcosβ/cosαcosβ =
5cosαsinβ/cosαcosβ
即：tanα=5tanβ

追答

4、sin(θ + π/4)=
sin[θ + (π/2 - π/4)]=
sin(π/2 + θ - π/4)=
sin[π/2 + (θ - π/4)]=
cos(θ - π/4)
两边平方：(x+y)²=
[√2sin(θ + π/4)]²
x²+2xy+y²=2cos²(θ - π/4)
同理：x²-2xy+y²=2sin²(θ - π/4)
两式相加：2x² + 2y²=
2[cos²(θ - π/4) + sin²(θ - π/4)]
2(x² + y²)=2•1
∴x² + y²=1

Answer 2