Hola!!!! userssolve this ✴i want correct option with proper solution ✌✌✌. Created by TheUrvashi. Math

Hola!!!! userssolve this ✴i want correct option with proper solution ✌✌✌...

AneekBiswas1 $\mathit{{HELLO\:\: DEAR,}}\\\\ \\ GIVEN \:\:THAT:-\\sec\theta = 13/5 \\\\ \\ sec^2\theta = 1 + tan^2\theta\\\\ \\ tan^2\theta = \frac{139 - 25}{25}\\\\ \\ tan^2\theta = \frac{144}{25}\\\\ \\ tan\theta = \frac{12}{5}$

NOW,

$\mathit{ DIVIDE \: \: BY \: \: COS\theta \: \: IN \: \: NUMERATOR \: \: AND \: \: DENOMINATOR}\\\\ \\ \mathit{\frac{\frac{2sin\theta - 3cos\theta}{cos\theta}}{\frac{4sin\theta - 9cos\theta}{cos\theta}} = \frac{2tan \theta - 3}{4tan \theta - 9} }$

$= \mathit{\frac{2*\frac{12}{5} - 3}{4*\frac{12}{5} - 9}}$

$= \mathit{ \frac{\frac{24 - 15}{5}}{\frac{48 - 45}{5}}}$

$= \mathit{\frac{\frac{9}{5}}{\frac{3}{5}}}$

$\mathit{=3}$

$\mathit{HENCE,\:\: OPTION\:\: (C)\:\: IS \:\: CORRECT}$

$\large{\mathit{\underline{I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}}}$