请帮忙prove trigonometry equation谢谢！

kthor

(tanx + secx - 1)/(tanx - secx + 1) = (1 + sinx)/(cosx)
这题怎么做？

mathlim

(tanx + secx - 1)/(tanx - secx + 1)
= (sinx + 1 - cosx)/(sinx - 1 + cosx)
= [2sin(x/2)cos(x/2) + 2sin^2(x/2)]/[2sin(x/2)cos(x/2) - 2sin^2(x/2)]
= [cos(x/2) + sin(x/2)]/[cos(x/2) - sin(x/2)]
= [cos(x/2) + sin(x/2)]^2/[cos^2(x/2) - sin^2(x/2)]
= [cos^2(x/2) + 2sin(x/2)cos(x/2) + sin^2(x/2)]/(cosx)
= (1 + sinx)/(cosx)

kthor

果然是高手！忘了还有 sin2x=2sinxcosx 和 cos2x=(cosx)^2-(sinx)^2
这两个Identities.
谢谢高手！