Question

解方程，要详细过程？

Answer 1

sin45°/sinθ=1/sin(75°-θ)
解:sinθ=sin45°sin(75°-θ)
=-1/2[cos(45°+75°-θ)-cos(45°-75°+θ)]
=-1/2[cos(120°-θ)-cos(θ-30°)
=-1/2[ cos120°cosθ+ sin120°sinθ-cosθcos30°- sinθsin30°]
=-1/2[-1/2cosθ+ √3/2sinθ-√3/2cosθ-1/2sinθ ]
=-1/2[(-1/2-√3/2)cosθ+(-1/2+ √3/2 )sinθ]
=(1+√3)/4cosθ+(1-√3)/4sinθ
sinθ-(1-√3)/4sinθ=(3+√3)/4sinθ=(1+√3)/4cosθ(移项，合并同类项)
sinθ/cosθ=(1+√3)/(3+√3)
tgθ=(1+√3)/(3+√3)=(3+3√3-√3-3)/6=√3/3
θ=30°，解方程所求角度θ=30°。

Answer 2

0.4x-(0.4x*0.5)=2
解：先算括号内的乘法，得：
0.4x-0.2x=2
合并同类项，得：
0.2x=2
方程两边同时除以0.2，得
x=10。

Answer 3

sin45° / sinθ = 1 / sin(75° - θ)
sin45°sin75°cosθ - sin45°cos75°sinθ = sinθ
sin45° = cos45° = √2 / 2
sin75° = (√6 + √2) / 4
cos75° = (√6 - √2) / 4
tanθ = √3 / 3
θ = 180°k +30°