Question

Решите уравнение 1+sin2x=cosx+sinx

Answer 1

1+sin2x=cosx+sinx\
1+2sinxcosx=cosx+sinx\
1+4sinxcosx+4sin^2xcos^2x=cos^2x+sin^2x+2sinxcosx\
1+4sinxcosx+(2sinxcosx)^2=1+sin2x\
0=(sin2x)^2+sin2x\
sin2x(sin2x+1)=0\
sin2x=0iff 2x=kpiiff x=kfrac{{pi}{2}\
sin2x=-1iff 2x=frac{{3}{2})pi+2kpiiff x=frac{{3}{4}}pi +kpi