Proof of Trig Identity

Date: 7/24/96 at 18:46:58
From: Robert James Spencer
Subject: Proof of Trig Identity

Dear Dr. Math,

I am having trouble proving trig identities.  Here is an example:

Prove the following is an identity (let t = theta)
(sin 2t + sin t)/(cos 2t + cos t + 1) = tan t

I tried:

(2sin t cos t + sin t)/(2cos^2 t - 1 + cos t + 1) = tan t
(2sin t cos t + sin t)/cos t(2cos t + 1)= tan t
sin t(2cos t +1)/ cos t(2cos t +1) = tan t    
*Is this step allowable?*

sin t/cos t = tan t
tan t = tan t

Thanks for your time.

 Jackie Spencer

Date: 7/25/96 at 6:6:35
From: Doctor Anthony
Subject: Re: Proof of Trig Identity

Yes, your working is perfectly OK.  You can cancel a factor from top 
and bottom rows as long as it is a factor of the whole top row and 
whole bottom row.

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/