I try to maximise a following function:
x[t_] :=
1/4 (-1 + a) + a/4 + 1/2 Sqrt[a - a^2] Cos[d] -
1/4 (1 - a) Cos[d + 2*t] + 1/4 a Cos[d - 2*t] +
1/2 Sqrt[a - a^2] Cos[2*t]
with respect to a and d. What is more, $t \in (0,\frac{\pi}{4})$. From NMaximize I know what the range of a and d should be (see figures, where, however, $t \in (0,\frac{\pi}{2})$),
but I am looking for the analytical formula.
I have written something like this
Maximize[{x[t], 0 < t < Pi/4, 4/5 < a < 1, 0 < d < Pi/2}, {a, d}]
(I have hoped that limiting the possible values of a and d will help Mathematica), but the output is the same as the input.
Does it mean that the Mathematica is not able to give the analytical form of the maximisation?