Question

cosx ≥ 1/√2 розвяжіть рівняння

Answer 1

$cos x geqfrac1{sqrt2}\ -1leqcos xleq1\ cos x=frac1{sqrt2}\ x=pmfrac{pi}4+2pi n\ x=frac{pi}6Rightarrowcos x=frac{sqrt3}2>frac1{sqrt2}\ x=frac{pi}3Rightarrowcos x=frac12<frac1{sqrt2}\ x=-frac{pi}6Rightarrowcos x=frac{sqrt3}2>frac1{sqrt2}\ xin[-frac{pi}4+2pi n;frac{pi}4+2pi n],quad ninmathbb{Z}$