已知sin(x/2)=2cos(x/2),求(cos2x)÷[﹙√2﹚cos(45°+x)]sinx
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 03:22:57
![已知sin(x/2)=2cos(x/2),求(cos2x)÷[﹙√2﹚cos(45°+x)]sinx](/uploads/image/z/2765093-5-3.jpg?t=%E5%B7%B2%E7%9F%A5sin%EF%BC%88x%EF%BC%8F2%EF%BC%89%3D2cos%EF%BC%88x%EF%BC%8F2%EF%BC%89%2C%E6%B1%82%EF%BC%88cos2x%EF%BC%89%C3%B7%5B%EF%B9%99%E2%88%9A2%EF%B9%9Acos%EF%BC%8845%C2%B0%2Bx%EF%BC%89%5Dsinx)
已知sin(x/2)=2cos(x/2),求(cos2x)÷[﹙√2﹚cos(45°+x)]sinx
已知sin(x/2)=2cos(x/2),求(cos2x)÷[﹙√2﹚cos(45°+x)]sinx
已知sin(x/2)=2cos(x/2),求(cos2x)÷[﹙√2﹚cos(45°+x)]sinx
∵sin(x/2)=2cos(x/2)
∴sin(x/2)/cos(x/2)=2
cos(x/2)/sin(x/2)=1/2
∴(cos2x)÷{[﹙√2﹚cos(45°+x)]sinx}
=(cos²x-sin²x)÷{[√2(cos45ºcosx-sin45ºsinx)]sinx}
=(cosx+sinx)(cosx-sinx)/[cosx-sinx)sinx]
=(cosx+sinx)/sinx
=cosx/sinx+1
=[cos²(x/2)-sin²(x/2)]/(2sinx/2cosx/2)+1
=cos(x/2)/(2sinx/2)-sin(x/2)/(2cosx)+1
=1/4-1+1
=1/4
祝进步!