球函数sina*cosa/（1-sina+cosa）的max，min及此时的a值

令t = sina*cosa/(1-sina+cosa) 。
分母：1-sina+cosa = (1+cosa)-sina = 2[cos(a/2)]^2 - sina
= 2[cos(a/2)]^2 - 2sin(a/2)cos(a/2)
= 2cos(a/2)·[cos(a/2) - sin(a/2)]
分子：sina*cosa = 2sin(a/2)·cos(a/2)·cosa
= 2sin(a/2)·cos(a/2)·{[cos(a/2)]^2 - [sin(a/2)]^2}
∴t = sin(a/2)·[cos(a/2) + sin(a/2)]
= sin(a/2)·cos(a/2) + [sin(a/2)]^2
= (1/2)·sina + 1/2 - (1/2)·cosa
= 1/2 + (√2/2)·sin(a - π/4)
∴最大值 = (1+√2)/2 ，此时sin(a - π/4) = 1 ，
a = 2kπ + 3π/4 ，k是任意整数 。
最小值 = (1-√2)/2 ，此时sin(a - π/4) = -1 ，
a = 2kπ - π/4 ，k是任意整数 。