Sin4x+2sin2x/2(cosx+cos3x)=? ;при x=30

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To find the value of the expression given x = 30 degrees, we first need to convert the degrees to radians.

30 degrees = 30 * π / 180 radians
= π / 6 radians

Now we substitute this value into the expression:

Sin(4π/6) + 2Sin(2π/6) / 2(Cos(π/6) + Cos(3π/6))
= Sin(2π/3) + 2Sin(π/3) / 2(Cos(π/6) + Cos(π/2))
= Sin(120°) + 2Sin(60°) / 2(Cos(30°) + Cos(90°))
= Sin(2π/3) + 2Sin(π/3) / 2(Cos(π/6) + Cos(π/2))
= √3/2 + 2√3/2 / 2(√3/2 + 0)
= √3/2 + √3 / √3

= (2√3 + 3) / 2√3

Therefore, Sin(4x) + 2Sin(2x) / 2(Cosx + Cos3x) = (2√3 + 3) / 2√3 when x = 30 degrees.