Question

Решить сos5xcosx-sin5xsinx<-0,5

Answer 1

$cos5x\cdot cosx-sin5x\cdot sinx\ \textless \ -0,5\\\\cos(5x+x)\ \textless \ -0,5\\\\cos6x\ \textless \ -0,5\\\\\frac{2\pi}{3}+2\pi n\ \textless \ 6x\ \textless \ \frac{4\pi }{3}+2\pi n\; ,\; n\in Z\\\\\frac{\pi }{9}+\frac{\pi n}{3}\ \textless \ x\ \textless \ \frac{2\pi }{9}+\frac{\pi n}{3}\; ,\; n\in Z$