(a) \(\cos 3210^\circ\)
(b) \(\sin 6000^\circ\)
(c) \(\tan 8880^\circ\)
Rešitev: (a) \(\cdots=\cos 30^\circ = \frac{\sqrt{3}}{2}\), (b) \(\cdots=-\sin 60^\circ = -\frac{\sqrt{3}}{2}\), (c) \(\cdots=\tan 60^\circ = \sqrt{3}\)(a) \(\sin \frac{39\pi}{4}\)
(b) \(\cot \frac{25\pi}{3}\)
Rešitev: (a) \(\cdots=-\sin \frac{\pi}{4} = -\frac{\sqrt{2}}{2}\), (b) \(\cdots=\cot \frac{\pi}{3}= \frac{\sqrt{3}}{3}\)(a) \({\displaystyle\frac{\sin1230^\circ+\cos1230^\circ}{\cos300^\circ+\sin900^\circ}}\)
(b) \({\displaystyle\frac{\sin\frac{15\pi}{4}}{\tan\frac{11\pi}{6}-\cot\frac{10\pi}{3}}}\)
Rešitev: (a) \(\cdots=1-\sqrt{3}\), (b) \(\cdots=\frac{\sqrt{6}}{4}\)(a) \((1-\sin x)(1+\sin x)(1+\tan^2 x)\)
(b) \({\displaystyle\Big(\frac{1}{\tan x}+\tan x\Big)\cdot \sin^2 x}\)
(c) \({\displaystyle\Big(\frac{1}{\sin x}-\sin x\Big)^{-1}\cdot \cot^2 x}\)
(d) \({\displaystyle\frac{\sin^3 x-\cos^3 x}{\sin x-\cos x}-1}\)
(e) \({\displaystyle\frac{\tan x}{\cos x-\frac{\textstyle1}{\textstyle\cos x}}+\sin x + \sin x \cot^2 x }\)
Rešitev: (a) \(\cdots=1\), (b) \(\cdots=\tan x\), (c) \(\cdots=\frac{1}{\sin x}\), (d) \(\cdots=\sin x \cos x\), (e) \(\cdots=0\)(a) \(\sin 2x (\tan x + \cot x)\)
(b) \(\tan 2x (\cot x - \tan x)\)
Rešitev: (a) \(\cdots=2\), (b) \(\cdots=2\)(a) \({\displaystyle\frac{(\sin x+\cos x)^2-1}{\cos 2x}}\)
(b) \({\displaystyle\frac{\sin x+\sin 2x}{1+\cos x+\cos 2x}}\)
(c) \({\displaystyle\frac{\frac{\textstyle\sin x}{\textstyle\cos x+1}}{\frac{\textstyle2\sin x}{\textstyle\sin 2x}-1}}\)
Rešitev: (a) \(\cdots=\tan 2x\), (b) \(\cdots=\tan x\), (c) \(\cdots=\cot x\)(a) \(\cos\alpha\)
(b) \(\cot\alpha\)
Rešitev: (a) \(\cos\alpha=\frac{21}{29}\), (b) \(\cot\alpha=\frac{21}{20}\)(a) \(\cos\alpha\)
(b) \(\tan\alpha\)
Rešitev: (a) \(\cos\alpha=-\frac{3}{4}\), (b) \(\tan\alpha=-\frac{\sqrt{7}}{3}\)(a) \(\cos7\alpha+\cos5\alpha\)
(b) \(\sin(\alpha+\frac{\pi}{4})-\sin(\alpha-\frac{\pi}{4})\)
Rešitev: (a) \(\cdots=2\cos6\alpha \cos\alpha\), (b) \(\cdots=\sqrt{2}\,\cos\alpha\)(a) \({\displaystyle\frac{\sin2x-\sin x}{\cos 2x+\cos x}}\)
(b) \({\displaystyle\frac{\sin x-\sin(x+20^\circ)}{\cos(x+20^\circ)-\cos x}}\)
(c) \({\displaystyle\frac{\cos(60^\circ+x)-\cos(120^\circ-3x)}{2\cos x}}\)
Rešitev: (a) \(\cdots=\tan\frac{x}{2}\), (b) \(\cdots=\cot(x+10^\circ)\), (c) \(\cdots=-\sin(2x-30^\circ)\)(a) \({\displaystyle\frac{\frac{1}{2}+\cos 2x}{\cos (x-30^\circ)}}\)
(b) \({\displaystyle\frac{2\sin x-\sqrt{2}}{2\cos x+\sqrt{2}}}\)
Rešitev: (a) \(\cdots=2\cos(x+30^\circ)\), (b) \(\cdots=\tan(\frac{x-45^\circ}{2})\)(a) \({\displaystyle\frac{\sin x+\cos(x-\frac{\pi}{6})}{\sin x+\sin(x-\frac{2\pi}{3})}}\)
(b) \({\displaystyle\frac{\sin(5x+30^\circ)+\cos x}{\cos 4x +\cos(60^\circ-2x)}}\)
Rešitev: (a) \(\cdots=\sqrt{3}\,\cot(x-\frac{\pi}{3})\), (b) \(\cdots=2\sin(x+30^\circ)\)(a) \(\cos 2x+\cos 4x+\cos 6x\)
(b) \({\displaystyle\frac{\sin 2x+2\sin 3x+\sin 4x}{4\sin 3x}}\)
(c) \({\displaystyle\frac{1+\cos x+\cos 2x}{\cos(\frac{3x-60^\circ}{2})+\cos(\frac{x+60^\circ}{2})}}\)
Rešitev: (a) \(\cdots=4\cos 4x \cos(x+30^\circ) \cos(x-30^\circ)\), (b) \(\cdots=\cos^2\frac{x}{2}\), (c) \(\cdots=2\cos(\frac{x+60^\circ}{2})\)(a) \(\cos7x \cos2x\)
(b) \(\sin5x \sin3x\)
(c) \(\sin3x \cos2x\)
(d) \(\cos5x \sin2x\)
Rešitev: (a) \(\cdots=\frac{1}{2}\cos9x+\frac{1}{2}\cos5x\), (b) \(\cdots=-\frac{1}{2}\cos8x+\frac{1}{2}\cos2x\), (c) \(\cdots=\frac{1}{2}\sin5x+\frac{1}{2}\sin x\), (d) \(\cdots=\frac{1}{2}\sin7x-\frac{1}{2}\sin3x\)(a) \(\sin7x \cos3x-\sin5x \cos x\)
(b) \(\sin6x \sin x+\cos5x \cos2x\)
(c) \(\sin6x \sin4x-\sin3x \sin x\)
Rešitev: (a) \(\cdots=\sin2x \cos8x\), (b) \(\cdots=\cos4x \cos x\), (c) \(\cdots=\sin7x \sin3x\)(a) \({\displaystyle\frac{\sin x-\cos x}{\sin x+\cos x}=\tan(x-45^\circ)}\)
(b) \({\displaystyle\frac{\sin x+\cos x}{\sin(x-15^\circ)+\cos(x+15^\circ)}=\sqrt{2}}\)
(c) \({\displaystyle\frac{1+\cos x+\cos 2x+\cos 3x}{\cos x}=4\cos\frac{x}{2}\cos\frac{3x}{2}}\)
