证明:2sin(π/4+a)sin(π/4-a)=cos2a

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证明:2sin(π/4+a)sin(π/4-a)=cos2a证明:2sin(π/4+a)sin(π/4-a)=cos2a证明:2sin(π/4+a)sin(π/4-a)=cos2a证明:左边=2[si

证明:2sin(π/4+a)sin(π/4-a)=cos2a
证明:2sin(π/4+a)sin(π/4-a)=cos2a

证明:2sin(π/4+a)sin(π/4-a)=cos2a
证明:左边=2[sin(π/4)cosa+cos(π/4)sina][sin(π/4)cosa-cos(π/4)sina]
=2[cosa/√2+sina/√2][cosa/√2-sina/√2]
=(cosa+sina)(cosa-sina)
=cos²a-sin²a
=cos(2a)
=右边
故原命题成立,证毕.