math
posted by mike on .
how would you prove that sin^2(a)cos^2(b)= sin^2(b)cos^2(a).
i'm not completely sure that this is right but i used the difference of two squares on it to get (sin(a)+cos(b))(sin(a)cos(b)) then after that i am stuck. please help

It will surprise you to see how easy this one is.
we know that sin^2 a + cos^2 a = 1
and sin^2 b + cos^2 b = 1
then
sin^2 a + cos^2 a = sin^2 b + cos^2 b
now let's "move" the terms cos^2 a and cos^2 b to get the needed equation
sin^2 a  cos^2 b = sin^2 b  cos^2 a
Done!