Question 136157
Factor cos^2x from the first and last term and factor sin^2x from the 2nd and 3rd term:
  cos^2x(cos^2y + sin^2y) + sin^2x(sin^2y + cos^2y)
Each of the (cos^2y + sin^2y) expressions are equal to 1:
  cos^2x(1) + sin^2x(1)
which is equal to
  cos^2x + sin^2x
which is equal to
  1
Q.E.D