0 \\1 + t^{-1} = 12t\\12t^2 - t - 1 = 0\\D = 1 + 4*12 = 49 = 7^2\\t_1_,_2 = \frac{1\pm7}{24} => t = \frac{1}{3} \\" alt="1 + \frac{1}{3^{ctg(x)}} = 4*9^{\frac{cos(x-\frac{\pi}{4}) }{\sqrt{2}sin(x)}}\\\frac{cos(x-\frac{\pi}{4}) }{\sqrt{2}sin(x)} = \frac{cos(x)+sin(x)}{2sin(x)} = \frac{ctg(x)}{2} + \frac{1}{2}\\ 1 + \frac{1}{3^{ctg(x)}} = 4*9^{\frac{ctg(x)}{2} + \frac{1}{2}}\\\\ 1 + \frac{1}{3^{ctg(x)}} = 4*9^{\frac{1}{2}} * 9^{\frac{ctg(x)}{2}}\\ 1 + \frac{1}{3^{ctg(x)}} = 12 * 3^{ctg(x)}\\\\3^{ctg(x)} = t > 0 \\1 + t^{-1} = 12t\\12t^2 - t - 1 = 0\\D = 1 + 4*12 = 49 = 7^2\\t_1_,_2 = \frac{1\pm7}{24} => t = \frac{1}{3} \\" align="absmiddle" class="latex-formula">
