已知向量a=(2cos(π/4-θ),1) b=(2sin2θ*cos(π/4-θ),cos4θ)满足ab=4√2+3/3,
问题描述:
已知向量a=(2cos(π/4-θ),1) b=(2sin2θ*cos(π/4-θ),cos4θ)满足ab=4√2+3/3,
θ∈(π/4,π/2) 求tan2θ 计算(2cos*θ/2-sinθ-1)/(√2sin(θ+π/4))的值
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)[2...