1
2(√2/2sinx+√2/2cosx)=1
sin(x+π/4)=1/2
x+π/4=π/6+2πn U x+π/4=5π/6+2πn
x=-π/4+π/6+2πn U x=-π/4+5π/6+2πn
x=-π/12+2πn,n∈z U x=7π/12+2πn,n∈z
2
2(√2/2sinx-√2/2cosx)=1
sin(x-π/4)=1/2
x-π/4=π/6+2πn U x-π/4=5π/6+2πn
x=π/4+π/6+2πn U x=π/4+5π/6+2πn
x=5π/12+2πn,n∈z U x=13π/12+2πn,n∈z
3
√2cosπ/4cosx+√2sinπ/4sinx-cosx=0,5
√2*1/√2*cosx+√2*1/√2*sinx-cosx=0,5
cosx+sinx-cosx=1/2
sinx=1/2
x=π/6+2πn,n∈z U x=5π/6+2πn,n∈z
8X + 3Y = 30
4X + 5Y = 22
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- 8X - 10Y = - 44
8X + 3Y = 30
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- 7Y = - 14
Y = 2 ( кг) один пакет борошна
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4Х + 10 = 22
4Х = 12
Х = 3 ( кг) один пакет сахара
Sin²a=1:(1+ctg²a)=1:(1+2-2√2+1)=1/(4-2√2)
cos²a=1-sin²a=1-1/(4-2√2)²=1-1/(24-16√2)=(23-16√2)/(24-16√2)
cos2a=cos²a-sin²a=(23-16√2)/(24-16√2) -1/(4-2√2)=
=(23-16√2)/8(3-2√2)-1/(4-2√2)==(23-16√2)(3+2√2)/8(9-8) - (4+2√2)/(16-8)=
=(23-16√2)(3+2√2)/8 - (4+2√2)/8=(69+46√2-48√2-64-4-2√2)/8=(1-4√2)/8