Question

Simplify:
$x^2+2\left(\cos ec\alpha \right)xy+y^2=0$

Answer 1

Given,

$x^2+2\left(\cos ec\alpha \right)xy+y^2=0$

or, $x^2+2\left(\cos ec\alpha \right)xy+y^2(\cos e{c}^2\alpha -{\cot }^2\alpha )=0$ [ Since $\cos e{c}^2\alpha -{\cot }^2\alpha =1$]

or, $(x+y\cos ec\alpha {)}^2=(y\cot \alpha {)}^2$

or, $x=y(\pm \cot \alpha -\cos ec\alpha )$.