Помогите пожалуйста! срочно! 4cos (x/2) * cos(x) = cos (x )/ sin (x/2). Created by dff45rt96. algebra-ru

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August 2022 1 13 Report

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

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Alexandr130398 ОДЗ:
$sin( \frac{x}{2}) \neq 0 \\ \\ \frac{x}{2} \neq \pi n \\ \\ x \neq 2 \pi n. \ n \in Z$

Решение:

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

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

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