Cho \(\tan x + \cot x = m\). Biết \({\tan ^4}x + {...

A

- Hướng dẫn giải

\(\begin{array}{l}{\tan ^4}x + {\cot ^4}x\\ = {\left( {{{\tan }^2}x + {{\cot }^2}x} \right)^2} - 2{\tan ^2}x{\cot ^2}x\\ = {\left( {{{\left( {\tan x + \cot x} \right)}^2} - 2\tan x\cot x} \right)^2} - 2\\ = {\left( {{m^2} - 2} \right)^2} - 2\\ = {m^4} - 4{m^2} + 4 - 2\\ = {m^4} - 4{m^2} + 2\\ \Rightarrow a + b + c + d = 1 + 0 + ( - 4) + 2 = - 1\end{array}\)