Precalculus
posted by Greg on .
Prove or disprove cos(x+y)cos(xy)=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?

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 
Sorry but I meant to say LS = cos^2xsin^2y

cos(x+y)cos(xy) = 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 (1sin^2 y)  (1cos^2 x) sin^2 y
cos^2x  cos^2x sin^2y  sin^2y + cos^2x sin^2y
cos^2x  sin^2y