Răspuns:
asa este!!
Explicație pas cu pas:
sin x+sin(π/2-x) =2sin((x+π/2-x)/2)cos ((x-π/2+x)/2)=
=2sin (π/4)cos (x-π/4)=
2*(√2/2)cos (x-π/4)=
√2cos (x-π/4)
dar cos (x-π/4)=cosα, ∈[-1;1] deci |cos (x-π/4)|∈[0;1]
atunci | sinx + cosx |=|√2 * cos (x-π/4)|=√2| cos(x-π/4)|≤√2*1=√2
