User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/existence

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/integrand

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/evaluation

User:GFauxPas/Sandbox/Zeta2/FourierSeries/

User:GFauxPas/Sandbox/Zeta2/Informal Proof

Trig Lemma

 * $\displaystyle \frac {1 + \tan \frac x 2}{1 - \tan \frac x 2} = \sec x + \tan x$

Is there an easy way to prove this? I tried some trig identities and came up with only dead ends. Wolfram Alpha's approach is nightmarish.

Context is using Weierstrass Substitution for Primitive of Secant Function.

--GFauxPas (talk) 22:53, 22 July 2014 (UTC)


 * Guess: try multiplying top and bottom by $1 + \tan \frac x 2$ which will give you $1 - \tan^2 \frac x 2$ on the bottom ... not sure whether that helps or not.


 * Or there's Sum of Secant and Tangent and the Half Angle Formulas which may help. --prime mover (talk) 23:17, 22 July 2014 (UTC)


 * I got it, thanks for your ideas!:

Lemma? Or put it underMinor Trigonometric Identities? --GFauxPas (talk) 01:13, 23 July 2014 (UTC)