Question

1. cos^2x+3sin^2x+2корень из 3 sinxcosx=1

2. sinx+sin3x=sin5x+sinx

3. sinxcosx+cos^2 x=0

4. 2cos^2x+5cosx+2=0

Answer 1

$1. cos^2+3sin^2+2sqrt3sinx*cosx=1;\ cos^2x+3sin^x+2sqrt3sinx*cosx-sin^2x-cos^x=0;\ 2sin^2x+2sqrt3sinx*cosx=0 |:cosx;\ 2tg^2x+2sqrt3tgx=0;\ 2tgx(tgx+sqrt3)=0;\ 2tgx=0; x=pi*n;\ tgx+sqrt3=0;\ tgx=-sqrt3; x=-frac{pi}{3}+2*pi*n;$

$3. sinx*cosx+cos^2x=0 |:cos^2x;\ tgx+1=0;\ tg=-1; x=-frac{pi}{4}+pi*n.\ \ \ 4.\ 2cos^x+5cosx+2=0 cosx=t, |t|leq1;\ 2t^2+5t+2=0;\ D=25-16=9;\ t_1=frac{-5+3}{4}=-frac{1}{2};\ t_2=frac{-5-3}{4}=-2 - lishnii;\ cosx=-frac{1}{2}; x=+-pi-frac{pi}{3}+2pi*n$