Question

пожалуйста помогите как можно быстрее 9 и 10 задания.

Answer 1

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.