Question

A,B是锐角,cos(A-B)=√2/2,sin(A-π/4)=(-√6+√2)/4,求角2B-A的值

Answer 1

sinacosπ/4-cosasinπ/4=(-√6+√2)/4

√2/2(sina-cosa)=(-√6+√2)/4

sina-cosa=(-√3+1)/2

两边平方

sin²a+cos²a-2sinacosa=(3+1-2√3)/4

1-sin2a=(2-√3)/2

sin2a=√3/2

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