Question

已知向量a=(sinθ,cosθ-2sinθ),b=(1.2)若|向量a|=|向量b|，0<θ<π，求θ的值.

Answer 1

|a|=|b|
(sinθ)^2+(cosθ-2sinθ)^2 = 5
4(sinθ)^2-4sinθcosθ -4=0
-2sin2θ - 2(1-2(sinθ)^2)-2=0
-2sin2θ - 2cos2θ-2=0
sin2θ +cos2θ=-1
√2(sin(2θ+π/4)=-1
2θ+π/4 = 5π/4 or 7π/4
θ = π/2 or 3π/4

Answer 2

|a|=|b|
|a|²=|b|²
sin²θ+(cosθ-2sinθ)²=5
cos²θ-4sinθcosθ+5sin²θ=5
4cos²θ=-4sinθcosθ
sinθ=-cosθ
θ=3π/4