After simplification, you get

cos^4(x)*sin^2(y) +sin^4(x)*cos^2(y) = sin^2(y)*cos^2(y)

cos^4(x)*sin^2(y) +[1-cos^2(x)]^2*cos^2(y) = sin^2(y)*cos^2(y)

cos^4(x)*sin^2(y) +[1-2cos^2(x) + cos^4(x)] *cos^2(y) = sin^2(y)*cos^2(y)

cos^4(x)*sin^2(y) +cos^2(y)-2cos^2(x)*cos^2(y) + cos^4(x)*cos^2(y) = sin^2(y)*cos^2(y)

cos^4(x)*[sin^2(y) +cos^2(y)]-2cos^2(x)*cos^2(y) = sin^2(y)*cos^2(y) - cos^2(y)

cos^4(x) - 2cos^2(x)*cos^2(y) = [sin^2(y) - 1]*cos^2(y)

cos^4(x) - 2cos^2(x)*cos^2(y) = - cos^4(y)

cos^4(x) - 2cos^2(x)*cos^2(y) + cos^4(y) = 0

[cos^2(x) - cos^2(y) = 0

cos^2(x) = cos^2(y)

1 - cos^2(x) = 1 - cos^2(y)

sin^2(x) = sin^2(y)

Substitute this value in the other expression and find the value.