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