已知-π/2≤а＜B≤π/2,求(a+b)/2、(a-b)/2的取值范围

已知-π/2≤а＜B≤π/2,求(a+b)/2、(a-b)/2的取值范围
已知-π/2≤а＜B≤π/2,求(a+b)/2、(a-b)/2的取值范围

已知-π/2≤а＜B≤π/2,求(a+b)/2、(a-b)/2的取值范围
∵-π/2≤а＜B≤π/2
∴-π/2≤а＜π/2,-π/2＜b≤π/2
两式相加
可得-π/＜a+b≤π/
即-π/2＜(a+b)/2≤π/2
∵-π/2≤а＜b≤π/2
∴-π/2≤а＜π/2,-π/2≤-b＜π/2
两式相加
可得-π≤а-b＜π
而a