Trigonometry's power

$\log_{(192\cos{x})}192\sin{x}=\dfrac{4}{5}$

$192\sin{x}=(192\cos{x})^{\frac{4}{5}}$

$192\sin{x}=\dfrac{192\cos{x}}{(192\cos{x})^{\frac{1}{5}}}$

$(192\cos{x})^{\frac{1}{5}}=\dfrac{192\cos{x}}{192\sin{x}}$

$(192\cos{x})^{\frac{1}{5}}= \cot x$

$(192\cos{x})^{\frac{4}{5}}= \cot^{4}x$

$192\sin{x}= \cot^{4}x$

$192\sin{x}= \dfrac{\cos^{4}x}{\sin^{4}x}$

$192\sin^{5}{x}= \cos^{4}x$

$192\sin^{5}{x}= (1-\sin^{2}x)^{2}$

$192\sin^{5}{x}-(1-\sin^{2}x)^{2} =0$

$(3\sin x-1)(64\sin^{4}x+21\sin^{3}x+7\sin^{2}x+3\sin x+1)=0$

$\Rightarrow 3\sin x-1 =0$

$\Rightarrow \sin x = \frac{1}{3}$

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$\cot^{4}x= 192(\frac{1}{3})=64$

$y=32(\cot^{4}x-1)=32(64-1)=2016$