Question

Решите неравенство sinx+cosx≤1.

Answer 1

$sinx+cosx leq1;$
$frac{1}{ sqrt{2}} sinx+ frac{1}{ sqrt{2}}cosx leq frac{1}{ sqrt{2}};$
$cos frac{ pi }{4}sinx+sin frac{ pi }{4}cosx leq frac{1}{ sqrt{2}};$
$sin(x+ frac{ pi }{4}) leq frac{1}{ sqrt{2}};$
$frac{3 pi }{4}+2 pi n leq x+ frac{ pi }{4} leq frac{9 pi }{4}+2 pi n;$
$frac{pi }{2}+2 pi n leq x leq 2 pi +2 pi n;$
$[frac{pi }{2}+2 pi n ; 2 pi +2 pi n;]$