Тригонометрическое неравенство:sinx-cosx больше 1

[latex]sinx>1+cosx\\ sin^2x>1+2cosx+cos^2x\\ 1-cos^2x>1+2cosx+cos^2x\\ 2cos^2x+2cosx<0\\ 2cosx(cosx+1)<0\\ \left \{ {{cosx<0} \atop {cosx>1}} \right.\\ \left \{ {{cosx>0} \atop {cosx<1}} \right. \\\\ 2\pi\*n+\frac{\pi}{2}[/latex]