решите уравнение cos2x+sin(x+3p/2)=0

Question

решите уравнение cos2x+sin(x+3p/2)=0

Answer 1

cos2x+sin(x+3p/2)=0

cos^2x-sin^2x-cosx=0

2cos^2x-cosx-1=0

cosx=t

2t^2-t-1=0

D=9

x1=1

x2=-1/2

cosx=1        cosx=-1/2

x=2pik           x=+-2pi/3+2pik