Question

ECUACIONES TRIGONOMETRICAS

Answer 1

$\sin 4x>4\sin x\sin 2x \sin 3x\\\sin 4x>2(2\sin x\sin2x)\sin 3x\\\sin 4x>2(\cos x -\cos 3x)\sin 3x\\\sin 4x>2\sin 3x\cos x -2\sin 3x\cos 3x\\\sin 4x>\sin 4x +\sin 2x -\sin 6x\\\sin 6x-\sin 2x>0\\2\cos4x\sin 2x>0\\\\\cos4x\sin 2x>0\\(\cos 4x >0 \wedge \sin 2x>0)\vee (\cos 4x >0 \wedge \sin 2x>0)\\ \\x\in \left\langle -\dfrac{3\pi}{8},-\dfrac{\pi}{8}\right\rangle \cup \left\langle 0,\dfrac{\pi}{8}\right\rangle\cup \left\langle \dfrac{3\pi}{8},\dfrac{\pi}{2}\right\rangle$