π/6≤sin(2x-π/6)≤5π/6化简
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 05:21:18
![π/6≤sin(2x-π/6)≤5π/6化简](/uploads/image/z/13357339-43-9.jpg?t=%CF%80%2F6%E2%89%A4sin%282x-%CF%80%2F6%29%E2%89%A45%CF%80%2F6%E5%8C%96%E7%AE%80)
π/6≤sin(2x-π/6)≤5π/6化简
π/6≤sin(2x-π/6)≤5π/6
化简
π/6≤sin(2x-π/6)≤5π/6化简
因为
x∈(π/6,5π/12)
所以
2x+π/6∈(π/2,π)
得到
cos(2x+π/6)=-3/5
因此
cos(2x-π/12)= cos(2x+π/6-π/4)= cos(2x+π/6)cosπ/4 + sin(2x+π/6)sinπ/4
= √2/2*(-3/5+4/5)= √2/10
请采纳答案,支持我一下.