已知向量a=(2cos(π/4-θ),1) b=(2sin2θ*cos(π/4-θ),cos4θ)满足ab=4√2+3/
1个回答

(1)a*b=4cos(π/4-θ)*sin2θ*cos(π/4-θ)+cos4θ

=2[1+cos(π/2-2θ)]sin2θ+cos4θ

=2sin2θ+2(sin2θ)^2+cos4θ

=2sin2θ+1=(4√2+3)/3,

∴sin2θ=(2√2)/3,

2θ∈(π/2,π),

cos2θ=-1/3,

tan2θ=-2√2.

(2)[2cos^(θ/2)-sinθ-1]/[√2sin(θ+π/4)]

=[cosθ-sinθ]/[sinθ+cosθ]

=[(cosθ)^2-(sinθ)^2]/(1+sin2θ)

=cos2θ/(1+sin2θ)

=-3+2√2.