搜搜考试网三角变换求证
来源：学生作业帮 编辑：搜搜考试网作业帮 分类：数学作业 时间：2024/06/24 07:35:28
三角变换
求证
2/[1+tan(x/2)]
=2/[1+sin(x/2)/cos(x/2)]
=2cos(x/2)/[sin(x/2)+cos(x/2)] 注：分子、分母同乘以 cos(x/2)
=2cos(x/2)*[cos(x/2)-sin(x/2)]/{[cos(x/2)-sin(x/2)]*[sin(x/2)-cos(x/2)]}分子分母同乘以cos(x/2)-sin(x/2)
={2[cos(x/2)]^2-sinx}/{[cos(x/2)]^2 - [sin(x/2)]^2}
=[1+cosx-sinx]/cosx
=1/cosx + 1 - sinx/cosx
=secx + 1 -tanx
楼主的题目是错误的!
=2/[1+sin(x/2)/cos(x/2)]
=2cos(x/2)/[sin(x/2)+cos(x/2)] 注：分子、分母同乘以 cos(x/2)
=2cos(x/2)*[cos(x/2)-sin(x/2)]/{[cos(x/2)-sin(x/2)]*[sin(x/2)-cos(x/2)]}分子分母同乘以cos(x/2)-sin(x/2)
={2[cos(x/2)]^2-sinx}/{[cos(x/2)]^2 - [sin(x/2)]^2}
=[1+cosx-sinx]/cosx
=1/cosx + 1 - sinx/cosx
=secx + 1 -tanx
楼主的题目是错误的!