Question

решить уравнение 

cos14x+ 2sin5xsin9x=0

 

Answer 1

$cos14x+ 2sin5xsin9x=0$
$cos14x+ 2* frac{1}{2}(cos(5x-9x)-cos(5x+9x))=0$
$cos14x+ 2* frac{1}{2}(cos4x-cos14x)=0$
$cos14x+ cos4x-cos14x=0$
$cos4x=0$
$4x= frac{ pi }{2}+ pi k,$ $k$ ∈ $Z$
$x= frac{ pi }{8}+ frac{pi k}{4} ,$ $k$ ∈ $Z$