SOLUTION: cos^2xcos^2y+sin^2xsin^2y+sin^2xcos^2y+sin^2ycos^2x=1

Question 136157: cos^2xcos^2y+sin^2xsin^2y+sin^2xcos^2y+sin^2ycos^2x=1
Found 2 solutions by vleith, JSmall:
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
Given: cos^2xcos^2y+sin^2xsin^2y+sin^2xcos^2y+sin^2ycos^2x=1
We know that cos^2x + sin^2x = 1
cos^2xcos^2y+sin^2xsin^2y+sin^2xcos^2y+sin^2ycos^2x=1
cos^2xcos^2y+sin^2xcos^2y+sin^2xsin^2y+sin^2ycos^2x=1
(cos^2x + sin^2x)cos^2y+(sin^2x +cos^2x)sin^2y=1
(1)cos^2y+(1)sin^2y=1
cos^2y + sin^2y = 1
1 = 1 True!

Answer by JSmall(7) (Show Source): You can put this solution on YOUR website!
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
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