Question

2sinx=2cosx+sqrt6 Решить уравнение :)

Answer 1

2sinx=2cosx+sqrt(6)

2sin(x)-2cos(x)=sqrt(6)

sin(x)-cos(x)=sqrt(6)/2

sqrt(2)/2*sin(x)-sqrt(2)/2*cos (x)=sqrt(6)/2*sqrt(2)/2

sin(x)cos (pi/4)-cos(x)sin (pi/4)=sqrt(3)/2

sin(x-pi/4)=sqrt(3)/2

x-pi/4=(-1)^k*pi/3+pi*k, k є Z

x=pi/4+(-1)^k*pi/3+pi*k, k є Z