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[latex]5)\; \; sin(4x-\frac{\pi}{3})= \frac{1}{2} \\\\4x- \frac{\pi }{3} =(-1)^{n}\frac{\pi}{6}+\pi n,\; n\in Z\\\\4x=\frac{\pi}{3}+(-1)^{n}\frac{\pi}{6}+\pi n,\; n\in Z\\\\x=\frac{\pi}{12}+(-1)^{n}\frac{\pi}{24}+\frac{\pi n}{4},\; n\in Z\\\\6)\; \; 16-6sin^2 \beta -6cos^2 \beta =16-6\underbrace {(sin^2 \beta +cos^2 \beta )}_{1}=16-6=10\\\\7)\; \; y=4osx\\\\-1 \leq cosx \leq 1\\\\-4 \leq cosx \leq 4\\\\y\in [-4,4\, ]\\\\8)\; \; sin75+sin15=2sin45\cdot cos30=\sqrt2\cdot \frac{\sqrt3}{2}=\frac{\sqrt6}{2}[/latex] [latex]cos36+cos108=2cos72\cdot cos36=2\cdot \frac{\sqrt5-1}{4}\cdot \frac{\sqrt5+1}{4} =\\\\= \frac{5-1}{2\cdot 4} =\frac{1}{2} [/latex] [latex]sin 105-sin75=sin(90+15)-sin(90-15)=cos15-cos15=0[/latex]

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