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Strategies for Proving Trigonometric Identities

Date: 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

  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.


- Doctor Schwa, The Math Forum 
Associated Topics:
High School Trigonometry

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