Question

6^cos4x*6^cos6x=6^cos5x

Answer 1

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