已知1/cosa-1/sina=1,则sin2a的值为

1/cosa-1/sina = (sina - cosa)/(sina*cosa)
之后将上式平方得
(sin^2(a)+cos^2(a)-2sina*cosa)/[(sina*cosa)^2]
=(1-sin2a)/[sin^2(2a)/4] = 1
令sin2a = x
则4(1-x)/(x^2) = 1
=>4-4x = x^2
=>x^2+4x-4 = 0
=>x = [-4+sqrt(16+16)/2] = -2+2sqrt(2)
sqrt表示开平方！
另一根-2-2sqrt(2)舍掉！

根号2乘以sin（a+π/4）