Posted by **Greg** on Wednesday, November 14, 2012 at 3:07pm.

Prove or disprove cos(x+y)cos(x-y)=cos squared (x) - Sin squared (x)

I dstributed the cosines and attempted to cancel out terms but I can't get the signs right. Any help on what I am missing?

- Precalculus -
**Reiny**, Wednesday, November 14, 2012 at 4:14pm
LS

= [ cosxcosy - sinxsinx] [cosxcosy + sinxsiny]

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

= (cosxcosy)^2 - (sinxsiny)^2

RS = cos^2 x - sin^2x = cos 2x

doesn't look like they are equal

test with values:

let x = 60, y=45

LS = cos(105) cos(15 = -0.25

RS = cos^2 60 - sin^2 60 = +.25 ≠ LS

or

let x = 81, y= 50

LS = cos131 cos31 = -.5623..

RS = cos^2 81 - sin^2 81 = -.95.. ≠ LS

not an identity

- Precalculus -
**Greg**, Wednesday, November 14, 2012 at 4:19pm
Sorry but I meant to say LS = cos^2x-sin^2y

- Precalculus -
**Steve**, Wednesday, November 14, 2012 at 4:41pm
cos(x+y)cos(x-y) = cos^2 x - sin^2 y

(cosx cosy - sinx siny)(cosx cosy + sinx siny)

(cosx cosy)^2 - (sinx siny)^2

cos^2 x cos^2 y - sin^2 x sin^2 y

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

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

cos^2x - sin^2y

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