Question

if 2xcosa=3 and 3 tana=2y find relation between x and y by eliminating a​

Answer 1

$\bull \: \: \: \LARGE \bf{Given :}$

$\sf \to \: 2x \cos \theta = 3 \\ \to \sf 3 \tan \theta = 2y$

$\bull \: \: \: \LARGE \bf{Solution :}$

$\large\sf \: 2x \cos \theta = 3 \\ \\ \implies \sf x \cos \theta \: = \frac{3}{2} \\ \\ \large \: \implies\sf \: { \cos}^{2} \theta = \frac{9}{4 {x}^{2} } \\ \\ \large\implies \sf \: { \sec}^{2} \theta = \frac{4 {x}^{2} }{9} \underline{ \: \: \: \: \: \: \: \: }(1)$

Again

$\sf \large \:3 \tan \theta = 2y \\ \\ \large \implies \sf \: { \tan}^{2} \theta = \frac{ 4{y}^{2} }{9} \underline{ \: \: \: \: \: \: \: \: }(2)$

$\sf \LARGE \underline{ Subtracting \: {eq}^{n} \: 1 \: and \: 2}$

$\sf\large \: { \sec}^{2} \theta - { \tan}^{2} \theta = \frac{4 {x}^{2} }{9} - \frac{4 {y}^{2} }{9} \\ \\ \implies \large \sf \: 1 = \frac{4 {x}^{2} }{9} - \frac{4 {x}^{2} }{9} \\ \\ \implies \sf \boxed{ \boxed {\mathfrak{4 {x}^{2} - 4 {y}^{2} = 9}}}$

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