cosx/2 - корень из 3sinx/2+1=0

Question

cosx/2 - корень из 3sinx/2+1=0

Answer 1

cosx/2 – sqrt(3)sinx/2+1=0

 

cos^2(x/4)-sin^2(x/4)-sqrt(3)*2*sin(x/4)*cos(x/4)+sin^2(x/4)+cos^2(x/4)=0

 

2cos^2(x/4)-2*sqrt(3)*sin(x/4)*cos(x/4)=0

cos^2(x/4)-sqrt(3)*sin(x/4)*cos(x/4)=0

 

 

1) cos(x/4)=0

x/4=pi/2+pi*n

x=2*pi+4*pi*n

 

2)  cos(x/4)=sqrt(3)*sin(x/4)

cos(x/4)/sin(x/4)=sqrt(3)

ctg(x/4)=sqrt(3)

x/4=arcctg(sqrt(3))+pi*n

x/4=pi/6+pi*n

x=2*pi/3+4*pi*n

 

 

 

 

Answer 2

(cos(x)/2) - корень(3*sin(x))/(2+1) = 0

x ∈ {2*пи*k+asin(корень(корень(13)-2)/корень(корень(13)+2))}, k ∈ Z