On Fri, 23 Jan 2009 00:41:45 -0800 (PST), Albert <email@example.com> wrote:
>This (I think) is the last trig proof I've to do (there may be some in >the next booklet though): > >(tan x + sec x - 1) / (tan x - sec x + 1) = (1 + sin x) / cos x > >I've tried turning the tan and sec into sin and cos but I can't >factorise the resulting fraction down to a denominator of cos x. Also, >I've tried rationalising the fraction but it can't be simplified. >What's a key idea I should consider to tackle this proof?
Another quick way to do this one (but still perhaps not the best way) is to rewrite the RHS as tan x + sec x (which, even though it looks less "elementary", at least vaguely matches the LHS), so that you are left with proving:
tan x + sec x - 1 = (tan x + sec x)(tan x - sec x + 1)