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

## Answer This Question

## Related Questions

- Precalculus with Trigonometry - Prove or disprove the following Identities: cos...
- tigonometry - expres the following as sums and differences of sines or cosines ...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- Precal - I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A...
- pre-cal - Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos ...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- Prove or Disprove - Cos(X+y)cos(x-y)= cos^2theta - sin^2theta I foiled the left ...
- math - Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t...
- math - prove the identity : cos^4 theta- sin ^4 thetaover sin squared theta cos ...
- precalculus - For each of the following determine whether or not it is an ...

More Related Questions