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Résolvez l'équation \((\cos x+1)(1-2\sin x)(tg\,{2x}+1)=0\) .
\( S=\left\{\pi,\, \dfrac{\pi}{6},\, \dfrac{7\pi}{8}\right\} \)
\( S=\left\{\pi+2k\pi,\, \dfrac{\pi}{6}+2k\pi,\, \dfrac{3\pi}{8}+k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\pi+2k\pi,\, \dfrac{\pi}{6}+2k\pi,\, \dfrac{5\pi}{6}+2k\pi,\, \dfrac{3\pi}{8}+k\dfrac{\pi}{2};\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\pi+2k\pi,\, \dfrac{\pi}{6}+2k\pi,\, \dfrac{5\pi}{6}+2k\pi,\, \dfrac{3\pi}{8}+2k\pi,\, \dfrac{7\pi}{8}+2k\pi;\, k\in\mathbb{Z}\right\} \)
A l'aide des formules, calculez \(\cos\left(\dfrac{7\pi}{12}\right)\) .
\( \dfrac{\sqrt{2}-\sqrt{6}}{4} \)
\( \dfrac{\sqrt{2}+\sqrt{6}}{4} \)
\( \dfrac{\sqrt{6}-\sqrt{2}}{4} \)
\( \dfrac{1+\sqrt{2}}{2} \)
Résolvez l'équation \(\sin x+\sin 4x =0\) .
\( S=\left\{2k\dfrac{\pi}{5},\, -\dfrac{\pi}{3}-2k\dfrac{\pi}{3};\, k\in\mathbb{Z}\right\} \)
\( S=\left\{-2k\dfrac{\pi}{3};\, k\in\mathbb{Z}\right\} \)
\( S=\left\{2k\dfrac{\pi}{5};\, k\in\mathbb{Z}\right\} \)
\( S=\left\{k\dfrac{\pi}{5};\, k\in\mathbb{Z}\right\} \)
Résolvez l'équation \(2\cos^2 x-3\cos x+1 =0\) .
\( S=\left\{1+2k\pi,\, \dfrac{1}{2}+2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{3}+2k\pi,\, 2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{3}+2k\pi,\, -\dfrac{\pi}{3}+2k\pi,\, 2k\pi;\, k\in\mathbb{Z}\right\} \)
Déterminez à l'aide du cercle trigonométrique la valeur de \(tg\, \dfrac{4\pi}{3} \).
\( \dfrac{4}{3} \)
\( \dfrac{1}{\sqrt{3}} \)
\( \sqrt{3} \)
\(-\sqrt{3} \)
Résolvez l'équation \(tg\, 2x-tg\, 3x=0\) .
\(S=\left\{0,\, -\pi\right\} \)
\( S=\left\{k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{4}+k\dfrac{\pi}{2},\, \dfrac{\pi}{6}+k\dfrac{\pi}{3};\, k\in\mathbb{Z}\right\} \)
Résolvez l'équation \(4\cos^4 x-5\cos^2 x+1 =0\) .
\( S=\left\{\dfrac{1}{4}+2k\pi,\, 1+2k\pi;\, k\in\mathbb{Z}\right\}\)
\( S=\left\{-\dfrac{\pi}{3}+2k\pi,\, \dfrac{\pi}{3}+2k\pi,\, 2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{-\dfrac{2\pi}{3}+2k\pi,\, -\dfrac{\pi}{3}+2k\pi,\, \dfrac{\pi}{3}+2k\pi,\, \dfrac{2\pi}{3}+2k\pi,\, \pi+2k\pi,\, 2k\pi;\, k\in\mathbb{Z}\right\} \)
\(S=\emptyset \)
A l'aide des formules, calculez \(\cos\left(\dfrac{5\pi}{12}\right)\) .
\( \dfrac{\sqrt{6}+\sqrt{2}}{4} \)
\( \dfrac{\sqrt{3}+\sqrt{2}}{2} \)
Résolvez l'équation \(2\sin^2{x}=1-\sin{x} \).
\( S=\left\{-1,\, \dfrac{1}{2}\right\} \)
\( S=\left\{\dfrac{\pi}{6},\, \dfrac{5\pi}{6},\, \dfrac{3\pi}{2}\right\} \)
\( S=\left\{\dfrac{\pi}{6}+2k\pi,\, \dfrac{3\pi}{2}+2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{6}+2k\pi,\, \dfrac{5\pi}{6}+2k\pi,\, \dfrac{3\pi}{2}+2k\pi;\, k\in\mathbb{Z}\right\} \)
A l'aide des formules, calculez \(\sin\left(\dfrac{7\pi}{12}\right) \).
