Question

2cosx+sqrt3=0
sin(2P-x)-cos(3P/2+x)+1=0
sin9P/4
cos(-4P/3)

Answer 1

$2cosx+sqrt3=0\cosx=-frac{sqrt3}{2}\x=pm arccos(-frac{sqrt3}{2})+2pi n\x=pmfrac{pi}{6}+2pi n, ; nin Z;\\sin(2pi-x)-cos(frac{3pi}{2}+x)+1=0\-sinx-sinx+1=0\-2sinx=-1\sinx=frac{1}{2}\x=(-1)^narcsinfrac{1}{2}+pi n\x=(-1)^nfrac{pi}{6}+pi n, ; nin Z;\\sinfrac{9pi}{4}=sin(frac{8pi}{4}+frac{pi}{4})=sin(2pi+frac{pi}{4})=sinfrac{pi}{4}=frac{sqrt2}{2};\\cos(-frac{4pi}{3})=cos(-(frac{3pi}{3}+frac{pi}{3}))=cos(pi+frac{pi}{3})=-cosfrac{pi}{3}=-frac{1}{2}.$