Question

Cho \(\tan\alpha+\cot\alpha=m\), hãy tính theo \(m\) :

a) \(\tan^2\alpha+\cot^2\alpha\)

b) \(\tan^3\alpha+\cot^3\alpha\)

Answer 1

a) \(tan^2\alpha+cot^2\alpha=\left(tan\alpha+cot\alpha\right)^2-2tan\alpha cot\alpha\)
\(=m^2-2\).
b) \(tan^3\alpha+cot^3\alpha=\left(tan\alpha+cot\alpha\right)\)\(\left(tan^2\alpha-tan\alpha cot\alpha+cot^2\alpha\right)\)
\(=m\left(tan^2\alpha+cot^2\alpha-tan\alpha cot\alpha\right)\)
\(=m\left(m^2-2-2\right)=m\left(m^2-3\right)\).