Trigonometrijske jednačine - zadaci sa rešenjima

Autor: Denitsa Dimitrova (Bulgaria)
Zadatak 1
$\cos(2x)-7\sin x-4=0$
Zadatak 2
$\cos2x-5\cos x+3=0,\ \ x\in \left[0,\frac{\pi}{2}\right]$
Zadatak 3
$\cos 2x-5\sin x-3=0$
Zadatak 4
$\cos 2x+6\sin x-5=0, x\in(0, \pi]$
Zadatak 5
$5\sin x-2\cos^2x-1=0$

$x\in\left[0,\frac{\pi}{2}\right]$
Zadatak 6
$3+\cos 2x+3\sqrt{2}\cos x=0$

$x\in(0,\pi)$
Zadatak 7
$\cos2x+\frac{1}{\sqrt{1+\ctg^2(x)}}=0$
Zadatak 8
$\sin^4x+\cos^4x=\frac{5}{8}, x\in [0, \pi]$
Zadatak 9
$\sin^3x-3\sin^2 x+3\sin x=1$
$x\in [0, \pi]$
Zadatak 10
$(\cos2x-1)\ctg^2x=-3\sin x$
$x\in[0,\pi)$

Zadatak 11
$3\cos16x+8\sin^22x\cdot \cos^22x-5=0$
$x\in[0,\pi]$
Zadatak 12
$\sin^2x-3\sin x\cos x+2\cos^2x=0$
$x\in [0,\frac{\pi}{2}]$
Zadatak 13
$\sin^2x-(\sqrt{3}+1)\sin x \cos x +\sqrt{3}\cos^2x=0$
$x \in [0, \pi]$
Zadatak 14
$\cos x+ \sin x = \frac{\sqrt{2}}{2}$
$x\in[0,\pi]$
Zadatak 15
$\sin 2x-\sqrt{3}\cos 2x=-\sqrt{3}$
Zadatak 16
$\sin 2x-\cos x=0$
Zadatak 17
$\sin 3x =\sin x$
$x\in[0,2\pi]$
Zadatak 18
$\sin x+\sin 3x=\sin 2x+\sin 4x$
$x\in[0,\pi]$
Zadatak 19
$\cos x + \cos 2x+\cos 3x = 0$
Zadatak 20
$\sin 4x+\sin20x-\sin12x=0$
Zadatak 21
$\sin 3x+\cos(x-\frac{\pi}{6})=2$
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