Question

Помогите пожалуйста! срочно! 4cos (x/2) * cos(x) = cos (x )/ sin (x/2)

Answer 1

ОДЗ:
$sin( frac{x}{2}) neq 0 \ \ frac{x}{2} neq pi n \ \ x neq 2 pi n. n in Z$

Решение:

$4cos frac{x}{2} * cosx = frac {cos x }{ sin frac{x}{2} } |*sin frac{x}{2} \ \ 4sin frac{x}{2}* cos frac{x}{2} *cosx=cosx \ \ 2sinx*cosx=cosx \ \ 2sinx*cosx-cosx=0 \ \ cosx(2sinx-1)=0 \ \ left [ {{cosx=0} atop {2sinx-1=0}} right. textless = textgreater left [ {{cosx=0} atop {sinx= frac{1}{2} }} right. \ \ x= frac{ pi }{2} + pi n \ \ x= frac{ pi }{6} + 2 pi n \ \ x= frac{5 pi }{6} + 2 pi n, n in Z$

$OTBET: frac{ pi }{2} + pi n ; frac{ pi }{6} + 2 pi n; frac{5 pi }{6} + 2 pi n, n in Z$