再世猪哥靓
幼苗
共回答了21个问题采纳率:90.5% 举报
mn=cosθ(√2+sinθ)-sinθcosθ
n^2=(√2+sinθ)^2+(cosθ)^2=3+2√2sinθ
|m+n|^2=(m+n)^2=m^2+2mn+n^2
=1+2【cosθ(√2+sinθ)-sinθcosθ】+(3+2√2sinθ)
=4+2√2(cosθ+sinθ)
=4+4sin(θ+π/4)
cos(θ/2+π/8)=-4/5,两边平方,得cos^2 (θ/2+π/8)=16/25
得1/2【cos(θ+π/4)+1】=16/25
得cos(θ+π/4)=7/25
θ∈(π,3π/2),则θ+π/4∈(5π/4,7π/4),
所以sin(θ+π/4)=-24/25
所以|m+n|=2/5
1年前
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