Expert: Paul Klarreich - 2/20/2009

Question
I have one question on my homework that I just can't figure out. Here goes:
(2sin^2 2x) + (cos 4x) = 1
My teacher said that if I find the right double angle identity for cos 4x I should be able to solve this in two steps; however, I keep ending up with 2, not 1. I appreciate your help.

Answer
Questioner:   Stefanie
Category:  Advanced Math
Private:  No
 
Subject:  Prove a trig identity
Question:  I have one question on my homework that I just can't figure out. Here goes:
(2sin^2 2x) + (cos 4x) = 1
My teacher said that if I find the right double angle identity for cos 4x I should be able to solve this in two steps; however, I keep ending up with 2, not 1. I appreciate your help.
 
(2sin^2 2x) + (cos 4x) = 1

Try  cos(2t) = 1 - 2 sin^2(t), then use  t = 2x:

cos(2(2x)) = 1 - 2 sin^2(2x)

cos(4x) = 1 - 2 sin^2(2x)

Your identity:

2 sin^2(2x) + cos 4x = 1

2 sin^2(2x) + 1 - 2 sin^2(2x) = 1

1 = 1