6^cos4x*6^cos6x=6^cos5x

Решите задачу:

$6^{cos4x}*6^{co6x}=6^{cos5x} \\ \\ 6^{cos4x+cos6x}=6^{cos5x} \\ \\ cos4x+cos6x=cos5x \\ \\ 2cos \frac{4x+6x}{2}*cos \frac{6x-4x}{2}=cos5x \\ \\ 2cos5x*cosx=cos5x \\ \\ 2cos5x*cosx-cos5x=0 \\ \\ 2cos5x(cosx-0.5)=0 \\ \\ cos5x=0 \\ \\ x= \frac{ \pi }{2}+ \pi k, k \in \infty \\ \\ cosx-0.5=0 \\ \\ cosx=0.5 \\ \\ x= +-\frac{ \pi }{6}+ \pi k, k \in \infty \\$