Odpowiedź:
[tex]d)\\\\sin(x)(4cos^2x-3)=0\\\\sin(x) (4 cos^2(x)-3)=0\\\\4 cos^2(x)-3=0 , sin(x)=0\\\\4 cos^2(x)=3 , sin(x)=0\\\\cos^2(x)=\frac{3}{4} ,sin(x)=0\\\\cos(x)=\frac{\sqrt{3} }{2} ,cos(x)=-\frac{\sqrt{3} }{2},sin(x)=0\\\\x=2\pi n_{1} +\frac{\pi }{6} ,x=2\pi n_{2}+\frac{11\pi }{6} ,x=2\pi n_{3}+\frac{5\pi }{6} ,\\\\x=2\pi n_{4}+\frac{7\pi }{6} ,x=\pi n_{5}[/tex]
[tex]c)\\\\\sqrt{sin(\frac{x}{2}+\frac{\pi }{4})^2 }=\frac{\sqrt{3} }{2} \\\\sin^2(\frac{x}{2} +\frac{\pi }{4} )=\frac{3}{4} \\\\sin(\frac{x}{2} +\frac{\pi }{4} )=\frac{\sqrt{3} }{2} ,sin(\frac{x}{2} +\frac{\pi }{4} )=-\frac{\sqrt{3} }{2}\\\\\frac{x}{2}+\frac{\pi }{4} =2\pi n_{1} +\frac{5\pi}{12} ,\frac{x}{2}+\frac{\pi }{4}=2\pi n_{2}+\frac{\pi }{3} ,sin(\frac{x}{2}+\frac{\pi }{4} )=-\frac{\sqrt{3} }{2} \\\\x=4\pi n_{1} +\frac{5\pi }{6}, x=4\pi n_{2} +\frac{\pi }{6},x=4\pi n_{3} +\frac{13\pi }{6}[/tex]
[tex],x=4\pi n_{4} +\frac{17\pi }{6}[/tex]
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Odpowiedź:
[tex]d)\\\\sin(x)(4cos^2x-3)=0\\\\sin(x) (4 cos^2(x)-3)=0\\\\4 cos^2(x)-3=0 , sin(x)=0\\\\4 cos^2(x)=3 , sin(x)=0\\\\cos^2(x)=\frac{3}{4} ,sin(x)=0\\\\cos(x)=\frac{\sqrt{3} }{2} ,cos(x)=-\frac{\sqrt{3} }{2},sin(x)=0\\\\x=2\pi n_{1} +\frac{\pi }{6} ,x=2\pi n_{2}+\frac{11\pi }{6} ,x=2\pi n_{3}+\frac{5\pi }{6} ,\\\\x=2\pi n_{4}+\frac{7\pi }{6} ,x=\pi n_{5}[/tex]
[tex]c)\\\\\sqrt{sin(\frac{x}{2}+\frac{\pi }{4})^2 }=\frac{\sqrt{3} }{2} \\\\sin^2(\frac{x}{2} +\frac{\pi }{4} )=\frac{3}{4} \\\\sin(\frac{x}{2} +\frac{\pi }{4} )=\frac{\sqrt{3} }{2} ,sin(\frac{x}{2} +\frac{\pi }{4} )=-\frac{\sqrt{3} }{2}\\\\\frac{x}{2}+\frac{\pi }{4} =2\pi n_{1} +\frac{5\pi}{12} ,\frac{x}{2}+\frac{\pi }{4}=2\pi n_{2}+\frac{\pi }{3} ,sin(\frac{x}{2}+\frac{\pi }{4} )=-\frac{\sqrt{3} }{2} \\\\x=4\pi n_{1} +\frac{5\pi }{6}, x=4\pi n_{2} +\frac{\pi }{6},x=4\pi n_{3} +\frac{13\pi }{6}[/tex]
[tex],x=4\pi n_{4} +\frac{17\pi }{6}[/tex]