How do you simplify sin^4 x - cos^4 xsin4x−cos4x?

1 Answer
sente
Feb 19, 2016

sin^4(x)-cos^4(x)=-cos(2x)sin4(x)−cos4(x)=−cos(2x)

Explanation:

Using the following

  • a^2-b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b)

  • sin^2(x) + cos^2(x) = 1sin2(x)+cos2(x)=1

  • cos(2x) = cos^2(x) - sin^2(x)cos(2x)=cos2(x)−sin2(x)

We have:

sin^4(x)-cos^4(x) = (sin^2(x)+cos^2x())(sin^2(x)-cos^2x())sin4(x)−cos4(x)=(sin2(x)+cos2x())(sin2(x)−cos2x())

=(1)(-cos(2x))=(1)(−cos(2x))

=-cos(2x)=−cos(2x)

Related questions
See all questions in Fundamental Identities
Impact of this question
8396 views around the world
You can reuse this answer
Creative Commons License