tan x /(1-cot x) + cot x /(1-tanx) = 1+ sec x csc x
问题描述：
tan x /(1-cot x) + cot x /(1-tanx) = 1+ sec x csc x
求证!
答
tanx/(1 - cotx) + cotx/(1 - tanx)= tanx/(1 - cosx/sinx) + cotx/(1 - sinx/cosx)= sinxtanx/(sinx - cosx) + cosxcotx/(cosx - sinx)= (sinxtanx - cosxcotx)/(sinx - cosx)= (sin²x/cosx - cos²x/sinx...[(sinx - cosx)(sin²x + sinxcosx + cos²x)]/[sinxcosx(sinx - cosx)] = (1 + sinxcosx)/(sinxcosx)这步没看懂TAT 求解立方差公式a³ - b³ = (a - b)(a² + ab + b²)，之后就约掉sinx - cosx