Logarithms and Trigonometric Functions

Geometry Level 3

It is known that sinx\sin x and cosx\cos x are both positive but are not equal. If logsinxcot2x+logcosxtanx=0\log_{\sin x} \cot^2 x + \log_{\cos x} {\tan x}=0, find the value of cos4x+cos2x+1\cos^4 x + \cos^2 x +1.

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