ĐKXĐ: \(x\notin\left\{\dfrac{\Omega}{2}+k\Omega;\Omega+k\Omega\right\}\)
(tanx+7)*tanx+(cotx+7)*cotx=-14
=>\(tan^2x+cot^2x+7\left(tanx+cotx\right)=-14\)
=>\(\left(tanx+cotx\right)^2-2\cdot cotx\cdot tanx+7\left(tanx+cotx\right)+14=0\)
=>\(\left(tanx+cotx\right)^2+7\left(tanx+cotx\right)+12=0\)
=>\(\left(tanx+\dfrac{1}{tanx}+3\right)\left(tanx+\dfrac{1}{tanx}+4\right)=0\)
=>\(\dfrac{tan^2x+3tanx+1}{tanx}\cdot\dfrac{tan^2x+4tanx+1}{tanx}=0\)
=>\(\left[{}\begin{matrix}tan^2x+3tanx+1=0\\tan^2x+4tanx+1=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}tanx=\dfrac{-3+\sqrt{5}}{2}\\tanx=\dfrac{-3-\sqrt{5}}{2}\\tanx=-2+\sqrt{3}\\tanx=-2-\sqrt{3}\end{matrix}\right.\)
=>\(x\in\left\{arctan\left(\dfrac{-3+\sqrt{5}}{2}\right)+k\Omega;arctan\left(\dfrac{-3-\sqrt{5}}{2}\right)+k\Pi;arctan\left(-2+\sqrt{3}\right)+k\Omega;arctan\left(-2-\sqrt{3}\right)+k\Omega\right\}\)