Marinada '22

[lang=hr] Nema mira ni u vozilu hitne pomoći. Vozač Mile ne dolazi do rješenja mozgalice:\\ Ako znamo da je $(1 + \sin x)(1 + \cos x) = \frac{5}{4}$ i $(1 - \sin x)(1 - \cos x) = \frac{a}{b} - \sqrt{c}$ te da su $a, b$ i $c$ prirodni brojevi takvi da su $a$ i $b$ relativno prosti, koliko iznosi umnožak $abc$? [/lang] [lang=en] Peace cannot be found even in the ambulance. Mile the chauffeur is having trouble with this brain teaser:\\ Supose $a, b$ and $c$ are positive integers such that $a$ and $b$ are relatively prime. Furthermore, let $(1 + \sin x)(1 + \cos x) = \frac{5}{4}$ and $(1 - \sin x)(1 - \cos x) = \frac{a}{b} - \sqrt{c}$. What is the value of $abc$? [/lang]