6.2 Proving Trigonometric Identities − Proofs (I)
Tuesday, April 16, 2013
Review: Simplify: (secx cscx − cotx)(sinx − cscx)
• Since numerical substitution does not ensure an identity, we must
use a proof method in showing trig identities.
Steps for proofs
• Set up as T chart, with each side labeled.
• Do not combine more than one step in a proof
• NEVER WORK ACROSS THE T-CHART (must work on each
side separately)
• May have to work on both sides, but start on complicated side
• Steps
 Express in terms of sine and/or cosine
 Express with common denominator, try factoring
 If degree 2 terms are used, think pythagorean
 Rearrange basic identities
 Multiply by conjugate (see later in notes)
Examples
Trigonometry (II) Page 1
1. Prove tan2x + 1 = sec2x
2. Prove
• Conjugates are expressions such as (sinx + 1) and (sinx − 1)
because when you multiply them:
Trigonometry (II) Page 2
•
because when you multiply them:
3. Prove
using conjugates
4. Prove
Trigonometry (II) Page 3
5. Prove:
Trigonometry (II) Page 4
Trigonometry (II) Page 5