Prove cos(x+y)*cos(x-y)=cos^2x - sin^2y?

Comments

  • sahsjingsahsjing

    cos(x+y)*cos(x-y)

    = (1/2)[cos(2x) + cos(2y)]

    = (1/2)[2cos^2x - 1 + 1 - 2sin^2y]

    = cos^2x - sin^2y

    ----------

    Ideas: 2cosAcosB = cos(A+B) + cos(A-B)

  • jayjay

    cos(x+y)*cos(x-y)=cos^2x - sin^2y

    [cosxcosy - sinxsiny]*[cosxcosy + sinxsiny]

    (cosxcosy)^2 - (sinxsiny)^2

    cos^2xcos^2y - sin^2xsin^2y

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

    cos^2x-cos^2xsin^2y-sin^2y+cos^2xsin^2y

    cos^2x-sin^2y => proven

Sign In or Register to comment.