Б)
![sintcost=-0,5](https://tex.z-dn.net/?f=sintcost%3D-0%2C5)
![sin^2t+cos^2t=1\\\\1=(sin^2t+cos^2t)^2=sin^4t+2sin^2tcos^2t+cos^4t\; \; \Rightarrow \\\\sin^4t+cos^4t=1-2(sintcost)^2=1-2\cdot (-0,5)^2=1-2\cdot 0,25=0,5](https://tex.z-dn.net/?f=sin%5E2t%2Bcos%5E2t%3D1%5C%5C%5C%5C1%3D%28sin%5E2t%2Bcos%5E2t%29%5E2%3Dsin%5E4t%2B2sin%5E2tcos%5E2t%2Bcos%5E4t%5C%3B+%5C%3B+%5CRightarrow+%5C%5C%5C%5Csin%5E4t%2Bcos%5E4t%3D1-2%28sintcost%29%5E2%3D1-2%5Ccdot+%28-0%2C5%29%5E2%3D1-2%5Ccdot+0%2C25%3D0%2C5)
a) Этот пункт сделан в предыдущем вопросе
[tex]1/2 \int\sin5x-sinx} \, dx =1/2 \int\sin5x} \, dx - 1/2 \int\ {sinx} \, dx =
=-cos5x/10+cosx/2
Синус разности: sin(п/4-х) = sin(п/4)*cosx - cos(п/4)*sinx = (cosx - sinx)/(кореньиз2)
Правая часть: 2*sin^2(п/4-x) = 2*(cosx - sinx)^2/2=(cosx - sinx)^2 =
<span>=cos^2(x) + sin^2(x) -2sinx*cosx = 1 - sin2x.</span>