Question

Cho \(tanx+cotx=4\). Rut gon bthuc \(A=\left(tanx+2cotx\right)^2+\left(2tanx+cotx\right)^2\)

Answer 1

\(\left(tanx+cotx\right)^2=16\Leftrightarrow tan^2x+cot^2x+2=16\Rightarrow tan^2x+cot^2x=14\)

\(A=tan^2x+4cot^2x+4+4tan^2x+cot^2x+4\)

\(A=5\left(tan^2x+cot^2x\right)+8=5.14+8=78\)