Т.к. pi<а<3pi/2, то а - угол третьей четверти, и sina<0, cosa<0, tga>0, ctga>0
sina=-0.6, cosa=-\sqrt(1-cos^2a)=-\sqrt{1-0,36}=-0.8
tga=sina/cosa=-0.6/(-0.8)=0.75
ctga=1/tga=4/3
<span>cos(\pi/3-a)=cos(\pi/3)cosa+sin(\pi/3)sina=\\ =1/2*(-0.8)+\sqrt3/2*(-0.6)=-2/5-3\sqrt3/10=-(4+3\sqrt3)/10</span>
1 способ решения:
![2sin(2x-4 \pi )= \sqrt{3} \\ \\ sin(2x-4 \pi )= \frac{\sqrt{3}}{2} \\ \\ 2x-4 \pi =(-1)^n* \frac{ \pi }{3}+ \pi n \\ 2x=(-1)^n* \frac{ \pi }{3}+ \pi n+4 \pi \\ \\ x=(-1)^n* \frac{ \pi }{6}+ \frac{ \pi n }{2}+2 \pi =(-1)^n* \frac{ \pi }{6} + \frac{ \pi n }{2} \\ \\ OTBET: (-1)^n* \frac{ \pi }{6} + \frac{ \pi n }{2} , \ n \in Z](https://tex.z-dn.net/?f=2sin%282x-4+%5Cpi+%29%3D+%5Csqrt%7B3%7D++%5C%5C++%5C%5C+sin%282x-4+%5Cpi+%29%3D++%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D+%5C%5C++%5C%5C+2x-4+%5Cpi+%3D%28-1%29%5En%2A+%5Cfrac%7B+%5Cpi+%7D%7B3%7D%2B+%5Cpi+n++%5C%5C+2x%3D%28-1%29%5En%2A+%5Cfrac%7B+%5Cpi+%7D%7B3%7D%2B+%5Cpi+n%2B4+%5Cpi+++%5C%5C++%5C%5C+x%3D%28-1%29%5En%2A+%5Cfrac%7B+%5Cpi+%7D%7B6%7D%2B+%5Cfrac%7B++%5Cpi+n+%7D%7B2%7D%2B2+%5Cpi++%3D%28-1%29%5En%2A+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%2B+%5Cfrac%7B++%5Cpi+n+%7D%7B2%7D++%5C%5C++%5C%5C+OTBET%3A+%28-1%29%5En%2A+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%2B+%5Cfrac%7B++%5Cpi+n+%7D%7B2%7D+%2C+%5C+n+%5Cin+Z)
2 способ решения: (по формулам приведения sin(α-4π)=sinα)
![2sin(2x-4 \pi )= \sqrt{3} \\ 2sin2x= \sqrt{3} \\ \\ sin2x= \frac{ \sqrt{3} }{2} \\ \\ 2x=(-1)^n* \frac{ \pi }{3} + \pi n \\ \\ x=(-1)^n* \frac{ \pi }{6} + \frac{ \pi n}{2} \\ \\ OTBET: \ (-1)^n* \frac{ \pi }{6} + \frac{ \pi n }{2} , \ n \in Z](https://tex.z-dn.net/?f=2sin%282x-4+%5Cpi+%29%3D+%5Csqrt%7B3%7D++%5C%5C+2sin2x%3D+%5Csqrt%7B3%7D+%5C%5C++%5C%5C+sin2x%3D++%5Cfrac%7B+%5Csqrt%7B3%7D+%7D%7B2%7D++%5C%5C++%5C%5C+2x%3D%28-1%29%5En%2A+%5Cfrac%7B+%5Cpi+%7D%7B3%7D+%2B+%5Cpi+n+%5C%5C++%5C%5C+x%3D%28-1%29%5En%2A+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%2B+%5Cfrac%7B+%5Cpi+n%7D%7B2%7D+%5C%5C+%5C%5C+OTBET%3A+%5C+%28-1%29%5En%2A+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%2B+%5Cfrac%7B+%5Cpi+n+%7D%7B2%7D+%2C+%5C+n+%5Cin+Z)