Question

решить ур-е: sin2x+cos2x=-1

Answer 1

$sin2x+cos2x=-1\ 2sinxcosx+cos^2x-sin^2x+1=0\ 2sinxcosx+cos^2x-sin^2x+sin^2x+cos^2x=0\ 2sinxcosx+2cos^2x=0\ 2cosx(sinx+cosx)=0\ cosx = 0\x= frac{pi}{2}+pi n\ sinx+cosx=0|:cosx\ tgx+1=0\ tgx=-1\ x=frac{-pi}{4}+pi k$