Question

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ПОМОГИТЕ ПОЖАЛУЙСТА ​

Answer 1

1)sin(x/2)=0,2

{x/2=π-arcsin(1/5)+2πn, n€Z, x/2=arcsin(1/5)+2πk, k€Z}

{x=2π-2arcsin(1/5)+4πn, n€Z, x=2arcsin(1/5)+4πk, k€Z}

2)cos(x+π/3)=1/2<=>sin(π/6-x)=1/2

π/6-x=2πn+arcsin(1/2), n€Z

{π/6-x=2πn+5π/6, n€Z или

π/6-x=2πk+π/6, k€Z}

{-x=2πn+2π/3, n€Z или

-x=2πk, k€Z}

{x=-2πn-2π/3, n€Z или

x=-2πk, k€Z}

3)sin(x+π/6)=0

x+π/6=πn, n€Z, x=πn-π/6, n€Z

4)cosx•cos(2x)-sinx•sin(2x)=-1

cos(3x)=-1, 3x=2πn+π, n€Z, x=2πn/3+π/3, n€Z

5)(1+sinx)(4-sinx)=0

4+3sinx-sin²x=0, [sinx=t], -t²+3t+4=0 <=> -(t-4)(t+1)=0, (t-4)(t+1)=0, => t1=4, t2=-1

sinx=4 => x=π-arcsin4+2πn, n€Z, x=arcsin4+2πk, k€Z

sinx=1 => x=2πt-π/2, t€Z