Sin2α=2sinα*cosα⇒sinα*cosα =(sin2α)/2. sin(π -α) =sinα
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9.
cosπ/9*cos2π/9*cosπ/3*cos4π/9 =(1/2)*cosπ/9*cos2π/9*cos4π/9=
(1/2)*sinπ/9*cosπ/9*cos2π/9*cos4π/9 / sinπ/9=
(1/4)*sin2π/9*cos2π/9*cos4π/9 / sinπ/9=(1/8)*sin4π/9*cos4π/9 / sinπ/9=
(1/16)*sin8π/9 / sinπ/9=(1/16)*sin(π-π/9) / sinπ/9=(1/16)*sinπ/9) / sinπ/9 =1/16.
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10. y =sinx/8 -sin(x/8 -π/2) =sinx/8 -sin(-(π/2 - x/8))=sinx/8 +cosx/8 =√2sin(x/8 +π/4).
T =16π.
* * * sin(x+T)/8 +π/4) =sin(x/8+π/4 +T/8) = sin(x/8+π/4).
T/8 =2π⇒T =16π.
![S = \int\limits^0_1 {3-x-2^{x}} \, dx = \int\limits^0_1 {3} \, dx - \int\limits^0_1 {x} \, dx - \int\limits^0_1 {2^{x}} \, dx =](https://tex.z-dn.net/?f=S+%3D+%5Cint%5Climits%5E0_1+%7B3-x-2%5E%7Bx%7D%7D+%5C%2C+dx+%3D+%5Cint%5Climits%5E0_1+%7B3%7D+%5C%2C+dx+-+%5Cint%5Climits%5E0_1+%7Bx%7D+%5C%2C+dx+-+%5Cint%5Climits%5E0_1+%7B2%5E%7Bx%7D%7D+%5C%2C+dx+%3D+)
= 3x|(0,1) - x^2/2 |(0,1) - 2^x/ln2|(0,1) = 3-0-1/2+0-2/ln2+1/ln2 = 2.5-1/ln2