已知x属于（0,兀）sinx十cosx=1／5,则tanx等于多少 一个解还是两个解,要过程.速度!

sinx + cosx = 1/5 ==> cosx = 1/5 - sinx
sin²x + cos²x = 1
sin²x + (1/5 - sinx)² = 1
25sin²x - 5sinx - 12 = 0
(5sinx - 4)(5sinx + 3) = 0
sinx = 4/5 或 sinx = - 3/5
因为0 < x < π,sinx在第一、二象限均为正数
所以sinx = 4/5
而cosx = ± √[1 - (4/5)²] = ± 3/5
当cosx = 3/5,sinx + cosx = 4/5 + 3/5 = 8/5 ≠ 1/5,舍掉
当cosx = - 3/5,sinx + cosx = 4/5 - 3/5 = 1/5,符合
所以tanx = (4/5)(- 3/5) = - 4/3