Use trigonometric identities to write each expression in terms of a single trigonometric function or a constant. simplify cos t sin t?

Thanks to the pre-existing addition and subtraction theorums, we can establish the identity:
sin(a+b) = sin(a)cos(b)+sin(a)cos(b)

Then, solving this, we get
sin(a+b) = 2(sin(a)cos(b))
sin(a)cos(b) = sin(a+b)/2

a=b, so
sin(a)cos(a) = sin(a+a)/2
sin(a)cos(a) = sin(2a)/2
Therefore, the answer is sin(2a)/2.