А14=a1+13d=140
s14=1/2(a1+a14)*14=1/2(2a1+13d)*14=1050
a1=140-13d 7(280-26d+13d)=7(280-13d)=1050 280-13d=150
13d=280-150=130 d=10
a1=140-130=10
2x^2+x+2<0
2x^2+x+2=0
Решим через дискриминант:
D=1^2-4*2*2=1-16= -15,D<0=>решений нет
![\frac{13Sin46,9^{0}-8Cos34,1^{0}}{Cos19^{0}}=\frac{13Sin(90^{0}-34,1^{0})-8Cos34,1^{0}}{Cos19^{0}}=\frac{13Cos34,1^{0}-8Cos34,1^{0}}{Cos19^{0}}=\frac{5Cos34,1^{0}}{Cos19^{0}}](https://tex.z-dn.net/?f=%5Cfrac%7B13Sin46%2C9%5E%7B0%7D-8Cos34%2C1%5E%7B0%7D%7D%7BCos19%5E%7B0%7D%7D%3D%5Cfrac%7B13Sin%2890%5E%7B0%7D-34%2C1%5E%7B0%7D%29-8Cos34%2C1%5E%7B0%7D%7D%7BCos19%5E%7B0%7D%7D%3D%5Cfrac%7B13Cos34%2C1%5E%7B0%7D-8Cos34%2C1%5E%7B0%7D%7D%7BCos19%5E%7B0%7D%7D%3D%5Cfrac%7B5Cos34%2C1%5E%7B0%7D%7D%7BCos19%5E%7B0%7D%7D)
Может задание выглядит так :
![\frac{13Sin469^{0}-8Cos341^{0}}{Cos19^{0}}=\frac{13Sin(360^{0}+109^{0})-8Cos(360^{0}-19^{0})}{Cos19^{0}}=\frac{13Sin109^{0} -8Cos19^{0}}{Cos19^{0}}=\frac{13Sin(90^{0}+19^{0})-8Cos19^{0}}{Cos19^{0}}](https://tex.z-dn.net/?f=%5Cfrac%7B13Sin469%5E%7B0%7D-8Cos341%5E%7B0%7D%7D%7BCos19%5E%7B0%7D%7D%3D%5Cfrac%7B13Sin%28360%5E%7B0%7D%2B109%5E%7B0%7D%29-8Cos%28360%5E%7B0%7D-19%5E%7B0%7D%29%7D%7BCos19%5E%7B0%7D%7D%3D%5Cfrac%7B13Sin109%5E%7B0%7D%20-8Cos19%5E%7B0%7D%7D%7BCos19%5E%7B0%7D%7D%3D%5Cfrac%7B13Sin%2890%5E%7B0%7D%2B19%5E%7B0%7D%29-8Cos19%5E%7B0%7D%7D%7BCos19%5E%7B0%7D%7D)
![=\frac{13Cos19^{0}-8Cos19^{0} }{Cos19^{0} }=\frac{5Cos19^{0}}{Cos19^{0} }=5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B13Cos19%5E%7B0%7D-8Cos19%5E%7B0%7D%20%7D%7BCos19%5E%7B0%7D%20%7D%3D%5Cfrac%7B5Cos19%5E%7B0%7D%7D%7BCos19%5E%7B0%7D%20%7D%3D5)