证明:2sin(π/4+a)sin(π/4-a)=cos2a

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/27 20:33:39
证明:2sin(π/4+a)sin(π/4-a)=cos2a
x){ٌ{fgio7NԄ1u5mmU_`gCO/{oQ4L&PQ6‰`u2 YA] D& V ՊK P&\JifgS[:qE3uLx[Sl @a

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.