40/60 +1/63, множество вариантов
2x^2-5x+4=0
D=(-5)^2-4*2*4=25-32=-7 D<0 - нет корней
<span>для решения этого примера воспользуемся двумя формулами:
</span>
![sin \alpha* cos \beta = \frac{1}{2} (sin ( \alpha - \beta) +sin( \alpha + \beta )) \\ sin \alpha -sin \beta =2(sin (\frac{ \alpha - \beta }{2} )+cos(\frac{ \alpha + \beta }{2} ))](https://tex.z-dn.net/?f=sin+%5Calpha%2A+cos+%5Cbeta+%3D++%5Cfrac%7B1%7D%7B2%7D+%28sin+%28+%5Calpha+-+%5Cbeta%29+%2Bsin%28+%5Calpha+%2B+%5Cbeta+%29%29+%5C%5C+%0Asin+%5Calpha+-sin+%5Cbeta+%3D2%28sin+%28%5Cfrac%7B+%5Calpha+-+%5Cbeta+%7D%7B2%7D+%29%2Bcos%28%5Cfrac%7B+%5Calpha+%2B+%5Cbeta+%7D%7B2%7D+%29%29)
<span>
cos 3x sin 7 x= cos 2 x sin 8 x
(sin4x+sin10x)/2=(sin6x+sin10x)/2
</span>sin4x+sin10x=sin6x+sin10x
sin4x+sin10x-sin6x-sin10x=0
sin4x-sin6x=0
-2sinx*cos5x=0
sinx=0,
<em><u>x=2πn,n∈Z</u></em>cos5x=0, 5x=(π/2)+2πn,
<em><u>x=(π/10)+(2πn/5),n∈Z</u></em>