Если почерк непонятный, напишите!
3а-6а+2а-1=3а-6а=-3а+2а=-1а-1; вроде так
tg3pi/4+2 cos 5 pi/3=
![tg(\frac{3Pi}{4})+2cos(\frac{5Pi}{3})=\\tg(Pi-\frac{Pi}{4})+2cos(2Pi-\frac{Pi}{3})=\\tg(Pi-\frac{Pi}{4})+2cos(Pi+\frac{2Pi}{3})=\\tg(-\frac{Pi}{4})+2cos(-\frac{Pi}{3})=\\=-tg(\frac{Pi}{4})+2cos(\frac{Pi}{3})=-1+2*(1/2)=0](https://tex.z-dn.net/?f=tg%28%5Cfrac%7B3Pi%7D%7B4%7D%29%2B2cos%28%5Cfrac%7B5Pi%7D%7B3%7D%29%3D%5C%5Ctg%28Pi-%5Cfrac%7BPi%7D%7B4%7D%29%2B2cos%282Pi-%5Cfrac%7BPi%7D%7B3%7D%29%3D%5C%5Ctg%28Pi-%5Cfrac%7BPi%7D%7B4%7D%29%2B2cos%28Pi%2B%5Cfrac%7B2Pi%7D%7B3%7D%29%3D%5C%5Ctg%28-%5Cfrac%7BPi%7D%7B4%7D%29%2B2cos%28-%5Cfrac%7BPi%7D%7B3%7D%29%3D%5C%5C%3D-tg%28%5Cfrac%7BPi%7D%7B4%7D%29%2B2cos%28%5Cfrac%7BPi%7D%7B3%7D%29%3D-1%2B2%2A%281%2F2%29%3D0)
<span>4sin7pi/6+ctg5pi/4=</span>
<span>![4sin(7pi/6)+ctg(5pi/4)=\\4sin(Pi+(pi/6))+ctg(Pi+(5pi/4))=\\4*(-sin(pi/6))+ctg(pi/4)=\\4*(-1/2)+1=\\=-2+1=-1](https://tex.z-dn.net/?f=4sin%287pi%2F6%29%2Bctg%285pi%2F4%29%3D%5C%5C4sin%28Pi%2B%28pi%2F6%29%29%2Bctg%28Pi%2B%285pi%2F4%29%29%3D%5C%5C4%2A%28-sin%28pi%2F6%29%29%2Bctg%28pi%2F4%29%3D%5C%5C4%2A%28-1%2F2%29%2B1%3D%5C%5C%3D-2%2B1%3D-1)
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2cos^2a-cos2a=
![2cos^2a-cos2a=\\2cos^2a-(cos^2a-sin^2a)=\\2cos^2a-(cos^2a-(1-cos^2a))=\\2cos^2a-(2cos^2a-1)=\\2cos^2a-2cos^2a+1=1](https://tex.z-dn.net/?f=2cos%5E2a-cos2a%3D%5C%5C2cos%5E2a-%28cos%5E2a-sin%5E2a%29%3D%5C%5C2cos%5E2a-%28cos%5E2a-%281-cos%5E2a%29%29%3D%5C%5C2cos%5E2a-%282cos%5E2a-1%29%3D%5C%5C2cos%5E2a-2cos%5E2a%2B1%3D1)
4sina*cosa*cos2a=
![4sina*cosa*cos2a=\\2*(2sina*cosa)*cos2a=\\2sin2a*cos2a=sin4a](https://tex.z-dn.net/?f=4sina%2Acosa%2Acos2a%3D%5C%5C2%2A%282sina%2Acosa%29%2Acos2a%3D%5C%5C2sin2a%2Acos2a%3Dsin4a)
найдите cos2a,если sina=1/корень из 3
![sina=1/\sqrt{3}\ => cos2a=1-2sin^2a=\\1-(1/\sqrt{3})^2=\\1-1/3=2/3](https://tex.z-dn.net/?f=sina%3D1%2F%5Csqrt%7B3%7D%5C+%3D%3E+cos2a%3D1-2sin%5E2a%3D%5C%5C1-%281%2F%5Csqrt%7B3%7D%29%5E2%3D%5C%5C1-1%2F3%3D2%2F3)
найдите sin2a,если cosa=-1/корень из 5 и pi/2
![sin2a,cosa=-1/\sqrt{5},\\Pi/2<a<pi\=,Pi<2a<2Pi=>sin2a<0\\sin2a=2sina*cosa=\\2*\sqrt{1-cos^2a}*cosa=\\2*\sqrt{1-1/5}*(-1/\sqrt{5})=-(2/\sqrt{5}*2/\sqrt{5})=\\=-2/5](https://tex.z-dn.net/?f=sin2a%2Ccosa%3D-1%2F%5Csqrt%7B5%7D%2C%5C%5CPi%2F2%3Ca%3Cpi%5C%3D%2CPi%3C2a%3C2Pi%3D%3Esin2a%3C0%5C%5Csin2a%3D2sina%2Acosa%3D%5C%5C2%2A%5Csqrt%7B1-cos%5E2a%7D%2Acosa%3D%5C%5C2%2A%5Csqrt%7B1-1%2F5%7D%2A%28-1%2F%5Csqrt%7B5%7D%29%3D-%282%2F%5Csqrt%7B5%7D%2A2%2F%5Csqrt%7B5%7D%29%3D%5C%5C%3D-2%2F5)
D=-b^2-4ac=9-4•2•0,5=5. 0,5=1/2