Expert: Paul Klarreich - 9/22/2008

Question
OK, so I have a few problems that I'm stuck on>>>>>>>>>>>>

This is from my trig book:
"Use trigonometric identities to write each expression in terms of a single trigonometric function or a constant. Answers may vary."

1. tan t cos t (for this one, I looked up the answer in the back of the book and the answer is: sin t)

2. 1 - sec^2 t

3. 1 - cos^2/tan^2 t

I can find the answers in the back of the book, but I don't understand how to calculate the problems.

Any help would be appreciated!


Answer
Questioner:   Sohail
Category:  Advanced Math
Private:  No
 
Subject:  Trig identities
Question:  OK, so I have a few problems that I'm stuck on>>>>>>>>>>>>

This is from my trig book:
"Use trigonometric identities to write each expression in terms of a single trigonometric function or a constant. Answers may vary."

1. tan t cos t (for this one, I looked up the answer in the back of the book and the answer is: sin t)

2. 1 - sec^2 t

3. 1 - cos^2/tan^2 t

I can find the answers in the back of the book, but I don't understand how to calculate the problems.

Any help would be appreciated!
==========================================================
Hi, Sohail,

For starters, there is a list of 'standard' identities.  You can find it in your text or online.  Use them:

1. tan t cos t =  (sin t/cos t) cos t = sin t   << quotient identity

2. 1 - sec^2 t = 1 - (1 + tan^2 t)  << Pythagorean id.

= 1 - 1 - tan^2 t =  - tan^2 t

         cos^2 t
3.  1 -   --------
         tan^2 t


           cos^2 t
   1 -   --------------
         sin^2 t/ cos^2 t

           cos^4 t
   1 -   ----------
           sin^2 t

   s^2 - (1 - s^2)^2
   -----------------
          s^2

   s^2 - (1 - 2s^2 + s^4)
   -----------------------
          s^2

   - 1 + 3 sin^2 t - sin ^4 t
   --------------------------
          sin^2 t

[there are other ways.]