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1) ![\frac{sin^2 \alpha }{cos \alpha -1} = \frac{1-cos^2 \alpha }{cos \alpha -1} = \frac{(1-cos \alpha)(1+cos \alpha)}{cos \alpha -1} =-1-cos \alpha \frac{sin^2 \alpha }{cos \alpha -1} = \frac{1-cos^2 \alpha }{cos \alpha -1} = \frac{(1-cos \alpha)(1+cos \alpha)}{cos \alpha -1} =-1-cos \alpha](https://tex.z-dn.net/?f=+%5Cfrac%7Bsin%5E2+%5Calpha+%7D%7Bcos+%5Calpha+-1%7D+%3D+%5Cfrac%7B1-cos%5E2+%5Calpha+%7D%7Bcos+%5Calpha+-1%7D+%3D+%5Cfrac%7B%281-cos+%5Calpha%29%281%2Bcos+%5Calpha%29%7D%7Bcos+%5Calpha+-1%7D+%3D-1-cos+%5Calpha+)
Ответ:![-1-cos \alpha -1-cos \alpha](https://tex.z-dn.net/?f=-1-cos+%5Calpha+)
2)![2cos^2x-1=2(1-sin^2x)-1=2-2sin^2x-1=1-2sin^2x = \\ =1-2*0,3=1-0,6=0,4 2cos^2x-1=2(1-sin^2x)-1=2-2sin^2x-1=1-2sin^2x = \\ =1-2*0,3=1-0,6=0,4](https://tex.z-dn.net/?f=2cos%5E2x-1%3D2%281-sin%5E2x%29-1%3D2-2sin%5E2x-1%3D1-2sin%5E2x+%3D+%5C%5C+%3D1-2%2A0%2C3%3D1-0%2C6%3D0%2C4)
Ответ:![0,4 0,4](https://tex.z-dn.net/?f=0%2C4)
3)![sin \frac{x}{2} = \frac{ \sqrt{2} }{2} \\ \\ \frac{ x_{1} }{2}= \frac{ \pi }{4} +2 \pi k \\ \\ \frac{ x_{2} }{2}= \frac{3 \pi }{4} +2 \pi k \\ \\ x_{1}= \frac{ \pi }{2} +4\pi k \\ \\ x_{2} = \frac{3 \pi }{2} +4 \pi k sin \frac{x}{2} = \frac{ \sqrt{2} }{2} \\ \\ \frac{ x_{1} }{2}= \frac{ \pi }{4} +2 \pi k \\ \\ \frac{ x_{2} }{2}= \frac{3 \pi }{4} +2 \pi k \\ \\ x_{1}= \frac{ \pi }{2} +4\pi k \\ \\ x_{2} = \frac{3 \pi }{2} +4 \pi k](https://tex.z-dn.net/?f=sin+%5Cfrac%7Bx%7D%7B2%7D+%3D+%5Cfrac%7B+%5Csqrt%7B2%7D+%7D%7B2%7D++%5C%5C++%5C%5C++%5Cfrac%7B+x_%7B1%7D+%7D%7B2%7D%3D+%5Cfrac%7B+%5Cpi+%7D%7B4%7D+%2B2+%5Cpi+k+%5C%5C++%5C%5C++%5Cfrac%7B+x_%7B2%7D+%7D%7B2%7D%3D+%5Cfrac%7B3+%5Cpi+%7D%7B4%7D+%2B2+%5Cpi+k+%5C%5C++%5C%5C++x_%7B1%7D%3D+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2B4%5Cpi+k++%5C%5C++%5C%5C++x_%7B2%7D+%3D+%5Cfrac%7B3+%5Cpi+%7D%7B2%7D+%2B4+%5Cpi+k)
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