How to factor the expression and use the fundamental identities to simplify 1-2cos^2x+cos^4x?

enrosca0fx

enrosca0fx

Answered question

2022-12-25

How to factor the expression and use the fundamental identities to simplify 12cos2x+cos4x?

Answer & Explanation

Tyrese Lang

Tyrese Lang

Beginner2022-12-26Added 4 answers

We need
(ab)2=a22ab+b2
sin2x+cos2x=1
Hence,
12cos2x+cos4x=(1cos2x)cos2x+cos4x
=1(1cos2x)cos2x(1cos2x)
=(1cos2x)(1cos2x)
=(1cos2x)2
=sin4x
mierekaslq

mierekaslq

Beginner2022-12-27Added 1 answers

Utilizing the Pythagorean identity, this is:sin2x+sin2x=112cos2x+cos4xcos4x=(1sin2x)2=12sin2x+sin4xcos2x=1sin2x12(1sin2x)+12sin2x+sin4x12+2sin2x+12sin2x+sin4x12+2sin2x+12sin2x+sin4x=sin4x

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?