On Fri, 23 Jan 2009 00:41:45 -0800 (PST), Albert <firstname.lastname@example.org> 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?
There may be a neater way to do it, but one fairly short way is to do the same first step as I suggested for the first problem, which is to rewrite A/B = C/D as AD = BC. The left hand side of the latter identity simplifies to 1 + sin x - cos x. Does the right hand side simplify to the same expression?