Question

Cho \(tanx+cotx=m\). Biết \(tan^4x+cot^4x=am^4+bm^3+cm^2+dm+e\) (a,b,c,d,e thuoc R). tính giá trị của \(T=a+b+c+d+e\)

Answer 1

\(\left(tanx+cotx\right)^2=m^2\)

\(\Leftrightarrow tan^2x+cot^2x+2=m^2\)

\(\Leftrightarrow tan^2x+cot^2x=m^2-2\)

\(\Rightarrow\left(tan^2x+cot^2x\right)^2=\left(m^2-2\right)^2\)

\(\Leftrightarrow tan^4x+cot^4x+2=m^4-4m^2+4\)

\(\Leftrightarrow tan^4x+cot^4x=m^4-4m^2+2\)

\(\Rightarrow a+b+c+d+e=1+0-4+0+2=-1\)