График функции f(x) = √x-4
<span>Sin(2x - 7</span>π<span>/2) + sin(3</span>π<span>/2 - 8x) + cos6x = 1 промежуток [0;</span>π<span>/2]
cos2x - cos8x + cos6x = 1
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cos2x + cos6x = 1+ cos8x
2cos4xcos2x = 2cos²4x
cos4x(cos4x - cos2x)=0
cos4x*2sin3x*sinx=0
<span>1)
cos4x = 0 </span>
4x = π/2 + πn<span>, </span>n Є Z
X = π/8 + πn/4<span>, </span>n Є Z
2) sin3x = 0
3x = πk, k Є Z
<span>X = πk/3, k Є Z</span>
<span>3)
sinx = 0</span>
X<span> = </span>πm, m Є Z
Так как серия х= Пk является частью серии<span> </span>πk/3, то отсюда
Ответ: <span> X </span><span>= π/8 + πn/4; X = πk/3</span>
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