Logarithms and Trigonometric Functions

Geometry Level 3

It is known that \(\sin x \) and \(\cos x\) are both positive but are not equal. If \(\log_{\sin x} \cot^2 x + \log_{\cos x} {\tan x}=0\), find the value of \(\cos^4 x + \cos^2 x +1\).

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