Question

if cotA = x/y then prove that xcosA-ysinA/xcosA+ysinA = x^2-y^2/x^2+y^2​

Answer 1

$\bf \large \bold{Hola!}$

• GiveN :

$\sf \mapsto \cot \: A \: = \frac{x}{y}$

_____________________________

• ShoW ThaT :

$\sf \mapsto \: \frac{x \cos \: A - y \sin \: A}{x \cos \:A + y \sin \: A } = \frac{ {x}^{2} - {y}^{2} }{ {x}^{2} + {y}^{2} }$

_____________________________

• ProoF :

$\boxed{ \sf{L\:H\:S}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \sf \cot \: A = \frac{x}{y}$

$\implies \sf \frac{ x \: \cos^{} \: A }{ y \: \sin ^{} \: A} = { (\frac{x}{y}) }^{2}$

$\sf \implies \: \frac{x \: \cos \: A \: - \: y \: \sin \: A}{x \: \cos \: A \: + \: y \: \sin \: A} = \frac{ {x}^{2} - {y}^{2} }{ {x}^{2} + {y}^{2} }$

$\implies \sf \boxed{ \sf \: \: { R \: H\: S}} \: \: \bf \: [ \: Proved \: ]$

______________________________

HOPE THIS IS HELPFUL...