Question

1+sinx+cosx+sin2x+cos2x=0

Answer 1

$1+sin leftxright+cos leftxright+sin left2xright+cos left2xright=0 \ 1+cos left2xright+cos leftxright+sin leftxright+2cos xleftxrightsin xleftxright=0 \ cos left xright +sin left xright+2cos ^2leftxright+2cos left xrightsinx leftxright=0 \ left(2cos left(xright)+1right)left(sin left(xright)+cos left(xright)right)=0$


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

$cos left(xright)=-frac{1}{2} ;x=frac{2pi }{3}+2pi n,:quad x=frac{4pi }{3}+2pi n \ sin(x)+cos(x)=0;quad x=frac{3pi }{4}+pi n$

$Otvet:x=frac{2pi }{3}+2pi n,:x=frac{3pi }{4}+pi n,:x=frac{4pi }{3}+2pi n$