Question

$frac{ 9^{sin2x}-3^{2 sqrt{2} sinx } }{ sqrt{11sinx} } =0$

Answer 1

$frac{9^{sin2x}-3^{2sqrt2sinx}}{sqrt{11sinx}}=0; ,\\ODZ:; ; sinx textgreater 0; ,; ; xin (2pi m; ;; pi +2pi m); ,; min Z\\(3^2)^{sin2x}-3^{2sqrt2sinx}=0\\3^{2sin2x}=3^{2sqrt2sinx}\\2sin2x=2sqrt2sinx\\4sinxcdot cosx-2sqrt2sinx=0\\2sqrt2sinxcdot (sqrt2cosx-1)=0\\a); ; sinx=0; ; to ; ; ; x=pi n,; nin Z\\b); ; cosx=frac{1}{sqrt2}=frac{sqrt2}{2}\\x=pm frac{pi}{4}+2pi k,; kin Z$

$c); ; left { {{x=pi n; ; ili; ; x=pm frac{pi }{4}+2pi k} atop {xin (2pi m; ;; pi +2pi m)}} right. ; ; ; Rightarrow x=frac{pi}{4}+2pi k,; kin Z$