![2Cos2x+4\sqrt{3}Cosx-7=0\\\\2(2Cos^{2}x-1)+4\sqrt{3}Cosx-7=0\\\\4Cos^{2}x-2+4\sqrt{3}Cosx-7=0\\\\4Cos^{2}x+4\sqrt{3}Cosx-9=0\\\\Cosx=m,-1 \leq m \leq 1 \\\\4m^{2} +4\sqrt{3}m-9=0](https://tex.z-dn.net/?f=2Cos2x%2B4%5Csqrt%7B3%7DCosx-7%3D0%5C%5C%5C%5C2%282Cos%5E%7B2%7Dx-1%29%2B4%5Csqrt%7B3%7DCosx-7%3D0%5C%5C%5C%5C4Cos%5E%7B2%7Dx-2%2B4%5Csqrt%7B3%7DCosx-7%3D0%5C%5C%5C%5C4Cos%5E%7B2%7Dx%2B4%5Csqrt%7B3%7DCosx-9%3D0%5C%5C%5C%5CCosx%3Dm%2C-1%20%5Cleq%20m%20%5Cleq%201%20%5C%5C%5C%5C4m%5E%7B2%7D%20%2B4%5Csqrt%7B3%7Dm-9%3D0)
![D=(4\sqrt{3})^{2}-4*4*(-9)=48+144=192=(8\sqrt{3})^{2}\\\\m_{1} =\frac{-4\sqrt{3}+8\sqrt{3}}{8} =\frac{4\sqrt{3} }{8} =\frac{\sqrt{3} }{2}\\\\m_{2}=\frac{-4\sqrt{3}-8\sqrt{3}}{8}=-\frac{12\sqrt{3} }{8}=-\frac{3\sqrt{3} }{2}<-1](https://tex.z-dn.net/?f=D%3D%284%5Csqrt%7B3%7D%29%5E%7B2%7D-4%2A4%2A%28-9%29%3D48%2B144%3D192%3D%288%5Csqrt%7B3%7D%29%5E%7B2%7D%5C%5C%5C%5Cm_%7B1%7D%20%3D%5Cfrac%7B-4%5Csqrt%7B3%7D%2B8%5Csqrt%7B3%7D%7D%7B8%7D%20%3D%5Cfrac%7B4%5Csqrt%7B3%7D%20%7D%7B8%7D%20%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%5C%5C%5C%5Cm_%7B2%7D%3D%5Cfrac%7B-4%5Csqrt%7B3%7D-8%5Csqrt%7B3%7D%7D%7B8%7D%3D-%5Cfrac%7B12%5Csqrt%7B3%7D%20%7D%7B8%7D%3D-%5Cfrac%7B3%5Csqrt%7B3%7D%20%7D%7B2%7D%3C-1)
Второй корень не подходит
![Cosx=\frac{\sqrt{3} }{2}\\\\x=\pm arcCos\frac{\sqrt{3} }{2}+2\pi n,n\in z\\\\x=\pm \frac{\pi }{6}+2\pi n,n\in z](https://tex.z-dn.net/?f=Cosx%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%5C%5C%5C%5Cx%3D%5Cpm%20arcCos%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%2B2%5Cpi%20n%2Cn%5Cin%20z%5C%5C%5C%5Cx%3D%5Cpm%20%5Cfrac%7B%5Cpi%20%7D%7B6%7D%2B2%5Cpi%20n%2Cn%5Cin%20z)
Тре-к МВР равнобедренный, углы РМВ и МРВ равны, обозначил их y.
Тре-к РКС равнобедренный тоже, углы РКС и КРС равны, их обозначим х.
Тогда угол ВРС развернутый равен 180 град, отсюда х+y+40=180 , x+y=140
MBP=180-2x
PCK=180-2y
BAC=180-MBP-PCK
Усё)
1.4х-3.5=2.2-0.6х-14.5
1.4х+0.6х=3.5+2.2-14.5
2х=-8.8
х=-8.8\2
х=-4.4
cos^2 Пи/8 - sin^2 Пи/8=cos Пи/4=корень из 2/2
Sin 15 градусов+cos 65 градусов=0,26593668610
sin40 градус-cos40 градус=0,63248845190
cos40 градус-sin16 градус=0,7691278761
cos18 градус-sin 22 градус=0,576449229
cos50 градус+sin80 градус=1,627595363
cos36 градус+sin36 градус=1,396802247
Ответы можно написать и покороче.