Marinada '25

[lang=hr] Nedaaa mi se više!! Kolikooo još imam???. geeez još dva zadatka. Ajde jedan brzinski cofffffe break pa ću nastavit .................................................................................................................................................................................. Ok idemoo daljeee! Ili možda bolje ne... Odredite maksimum funkcije $f(x)=\sin^{2025}x\cos x$ Za odgovor na ovaj zadatak za taj $x$ za koji se postiže maksimalna vrijednost izračunajte $f(x)^2$. Koji god broj dobijete pretvorite ga u potpuno skraćeni oblik razlomka $\frac{a}{b}$.(znači ako je cijeli broj, $b=1$, a $a$ je jednak tom cijelom broju) Izračunajte $a+b$. Ako je broj jako velik zapišite njegov ostatak pri dijeljenju s $1000007$. [/lang] [lang=en] I don’t feel like doing anything anymore!! How many more do I have??? Geez, two more problems. Let’s take a quick coffee break and then I’ll continue. .............................................................................................................................................................................. Okay, I’m moving on! Or maybe it’s better not to… Determine the maximum of the function $f(x)=\sin^{2025}x\cos x $ For the value of $x$ at which the maximum is attained, compute $f(x)^2$. Write whatever number you obtain as a fully reduced fraction $\dfrac{a}{b}$ (so if it is an integer, set $b=1$ and $a$ equals that integer). Calculate $a + b$. If the number is very large, give its remainder upon division by $1000007$. [/lang]