Ta có \(P = \ln \left( {\tan {1^0}.\tan {2^0}.\tan {3^0}...\tan {{89}^0}} \right).\)
Mặt khác
\(\tan x = \cot \left( {{{90}^0} - x} \right) \Rightarrow \tan x.\tan \left( {{{90}^0} - x} \right) = 1\)
\(\Rightarrow P = \ln \left( {\left( {\tan {1^0}.\tan {{89}^0}} \right) \left( {\tan {2^0}.\tan {{88}^0}} \right)...\tan {{45}^0}} \right) \Rightarrow P = \ln 1 = 0.\)