A Putnam Geometry Problem

[tshort]

[ QUOTE ]
then we want to maximize cos t (cos t + sin t). i believe that you can write this as a single trigonometric function, but it's simple enough to differentiate and get cos 2t - sin 2t, which implies that 2t = pi/4 or t = pi/8. now all that remains is to check that this is optimal.

[/ QUOTE ]

(cos t)^2 + sin(t)cost(t)

= (1+cos(2t))/2 + (sin(2t)+sin(0))/2)

= 1/2 + 1/2 cos2t + 1/2 sin2t

= 1/2 + Sqrt[1/2] cos(2t-Pi/4)

Then obviously this is maximized when 2t-Pi/4 = 0.