Sin^2x+cosx-1=o 1-3cos^2x=2sinx*cos x

1.
$sin^{2} x+cosx-1=1- cos^{2} x+cosx-1=cosx-cos^{2}x =\ \textgreater \ \\ cosx - cos^{2}x=0 \\ -cosx +cos^{2}x=0 \\ cosx(cosx-1)=0 \\ \left[\begin{array}{ccc}cosx=1\\cosx=0\end$
$x= \pi n- \pi /2 \\ x=2 \pi n$
2.
$1-3cos^{2}x=2sinxcosx|1=cos^2x+sin^2x \\ sin^{2}x-2cos^{2}x-2sinxcosx=0 | :cos^{2}x \\ tg^2x-2-2tgx=0 , ]tgx=n \\ n^2-2n-2=0, D=4+8=12 \\ n_{1} =1+ \sqrt{3} \\ n_{2}=1-\sqrt3 \\ tgx=1 \frac{+}{}\ \sqrt3 \\ x=artctg(1 \frac{+}{}\ \sqrt3)+ \pi k$
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