Question

tg²3x=3 помогите пожалуйста

Answer 1

$tg^23x=3\\ frac{sin^23x}{cos^23x}=3; ; ,; ; frac{1-cos6x}{1+cos6x}=3; ; ,; ; frac{1-cos6x}{1+cos6x}-3=0\\ frac{1-co6x-3-3cos6x}{1+cos6x}=0; ,; ; frac{-4cos6x-2}{1+cos6x}=0; ; ,; ; frac{2cos6x+1}{1+cos6x}=0; ,\\ left { {{2cos6x+1=0} atop {1+cos6xne 0}} right. ; ,\\cos6xne -1; ,; ; 6xne pi +2pi k; ,; ; xne frac{pi }{6}+frac{pi k}{3}; ,; kin Z\\2cos6x=1; ,; ; cos6x=-frac{1}{2} ; ,\\6x=pm (pi -frac{pi }{3})+2pi n=pm frac{2pi}{3}+2pi n; ,; nin Z$

$underline {x=pm frac{pi}{9}+frac{pi n}{3}; ,; nin Z}$