Strategies for Proving Trigonometric IdentitiesDate: 05/19/2003 at 18:01:42 From: Will Subject: Proving Trigonometric Identities In class this week, we learned about proving trig identities and we had a fair bit of homework relating to it. I was able to get most of them, but this question really stumped me. Prove the identity: 1 - sin x 1 --------- = tan x + ----- 1 + sin x cos x Date: 05/19/2003 at 18:23:49 From: Doctor Schwa Subject: Re: Proving Trigonometric Identities Hi Will, I have some basic tricks that I use when trying to prove trig identities. They are: 1) Rewrite everything in terms of sin and cos. (In your problem, this means converting tan x to sin x/cos x.) 2) Start by working on whichever side looks more complicated. 3) If you have fractions, always think about making common denominators. 4) When you have something with 1+sin or the like, think about multiplying top and bottom by the conjugate (1-sin). 5) Look for familiar identities like sin^2 + cos^2 = 1 that you can use. In this particular case, I think that if you start by multiplying the left side by (1-sin)/(1-sin), then something nice should happen. Or you may want to make a common denominator first. Give those hints a try, and see where they leads, then write back if you feel stuck again. Enjoy, - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/ |
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