Question

Solve the identity:

Answer 1

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

Answer 2

Not sure what the process for proving a trig equation is.

Answer 3

cos^2x + cos^2y +2cosxcosy + sin^2x + sin^2y -2sinxsiny
= cos^2x + sin^2x + cos^2y + sin^2y + 2cosxcosy - 2sinxsiny

Answer 4

now [ cos^2x + sin^2x =1 ]
hence we have
= cos^2x + sin^2x + cos^2y + sin^2y + 2cosxcosy - 2sinxsiny
= 1+1+ 2(cosxcosy - sinxsiny)
=2+2cos(x+y) [ cos(x+y) = cosxcosy - sinxsiny ]