Question

Вычислите Sin5xSin6x = Cosx

Answer 1

$\frac{1}{2} (cosx-cos11x)=cosx$
$cosx-cos11x=2cosx$
$cosx+cos11x=0$
$2cos6x*cos5x=0$
$cos6x=0$ или $cos5x=0$
$6x= \frac{ \pi }{2} + \pi k,$ k∈Z или $5x= \frac{ \pi }{2} + \pi n,$ n∈Z
$x= \frac{ \pi }{12} + \frac{\pi k}{6} ,$ k∈Z или $x= \frac{ \pi }{10} + \frac{\pi n}{5} ,$ n∈Z