先分析角度范围:因cos(θ+π/4)=√10/10>0且θ∈(0,π/2),则0由cos(θ+π/4)=cosθcosπ/4-sinθsinπ/4=√2/2(cosθ-sinθ)=√10/10,两边平方得sin2θ=4/5
由基本公式有cos2θ=√5/5,注意到0<2θ所以sin(2θ-π/4)=sin2θcosπ/4-cos2θsinπ/4=√2/2(sin2θ-cos2θ)=(4√2-√10)/10
先分析角度范围:因cos(θ+π/4)=√10/10>0且θ∈(0,π/2),则0由cos(θ+π/4)=cosθcosπ/4-sinθsinπ/4=√2/2(cosθ-sinθ)=√10/10,两边平方得sin2θ=4/5
由基本公式有cos2θ=√5/5,注意到0<2θ所以sin(2θ-π/4)=sin2θcosπ/4-cos2θsinπ/4=√2/2(sin2θ-cos2θ)=(4√2-√10)/10