已知sin-cos=1/2 则sin³−cos³的值为已知sin X-cosX=1/2 则sin³X−cos³X的值为
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/29 22:52:53
![已知sin-cos=1/2 则sin³−cos³的值为已知sin X-cosX=1/2 则sin³X−cos³X的值为](/uploads/image/z/13882568-32-8.jpg?t=%E5%B7%B2%E7%9F%A5sin-cos%3D1%2F2+%E5%88%99sin%26%23179%3B%26%238722%3Bcos%26%23179%3B%E7%9A%84%E5%80%BC%E4%B8%BA%E5%B7%B2%E7%9F%A5sin+X-cosX%3D1%2F2+%E5%88%99sin%26%23179%3BX%26%238722%3Bcos%26%23179%3BX%E7%9A%84%E5%80%BC%E4%B8%BA)
已知sin-cos=1/2 则sin³−cos³的值为已知sin X-cosX=1/2 则sin³X−cos³X的值为
已知sin-cos=1/2 则sin³−cos³的值为
已知sin X-cosX=1/2 则sin³X−cos³X的值为
已知sin-cos=1/2 则sin³−cos³的值为已知sin X-cosX=1/2 则sin³X−cos³X的值为
因:sinx-cosx=1/2 所以有:(sinx-cosx)²=1/4
得:sinxcosx=3/8
sin³X−cos³X
=(sinx-cosx)(sin²x+sinxcosx+cos²x)
=1/2(1+3/8)
=11/16
因为sin X-cosX=1/2 所以(sinX−cosX)²=(sin²X-2sinXcosX+cos²X)
=(1-2sinXcosX)
=1/4
所以sinXcosX=3/8
全部展开
因为sin X-cosX=1/2 所以(sinX−cosX)²=(sin²X-2sinXcosX+cos²X)
=(1-2sinXcosX)
=1/4
所以sinXcosX=3/8
所以sin³X−cos³X=(sinX−cosX)×(sin²X+sinXcosX+cos²X)
=1/2×(1+3/8)
=11/16
收起