Trig
posted by Max .
Simplify (sin^2)*(67.5deg)  (cos^2)*(67.5deg) and then evaluate exactly.

well, cos 2x = cos^2 x  sin^2 x, so what do you think?
If you end up with 1/√2 you are correct. 
How exactly do you get there though? I tried to follow a similar homework problem and got:
= (cos^2)*(67.5deg)  (sin^2)*(67.5deg)
= cos(2*67.5deg)
= cos135deg
= √2/2 
note that the problem was
sin^2(67.5)cos^2(67.5)
= cos(135)
my hint was not intended to make you forget what was originally asked. :)
And, I know lots of folks hate roots in the denominator, but I see no reason why √2/2 is better than 1/√2. Just mt preference 
Thank you very much!