若sinθ+cosθ=根号2 求log1/2(sinθ)·log1/2(cosθ)

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若sinθ+cosθ=根号2求log1/2(sinθ)·log1/2(cosθ)若sinθ+cosθ=根号2求log1/2(sinθ)·log1/2(cosθ)若sinθ+cosθ=根号2求log1/

若sinθ+cosθ=根号2 求log1/2(sinθ)·log1/2(cosθ)
若sinθ+cosθ=根号2 求log1/2(sinθ)·log1/2(cosθ)

若sinθ+cosθ=根号2 求log1/2(sinθ)·log1/2(cosθ)
sinθ+cosθ=根号2
两边平方,1+2sinθcosθ=2
2sinθcosθ=1
2sinθ(根号2-sinθ)=1
2sinθ^2-2根号2sinθ+1=0
sinθ=根号2/2
cosθ=根号(1-sinθ^2)=根号2/2
log1/2(sinθ)·log1/2(cosθ)
=(log1/2(根号2/2))^2
=(log1/2 (1/2)^(1/2))^2
=1/4

sinθ+cosθ=根号2*sin(a+45)=根号2
a=45+2kpi
用公式求角就O了