Question

Hola!!!! users

solve this
✴i want correct option with proper solution ✌✌✌

Answer 1

I gave answer one time.I am giving once more.Hope you like it.

Answer 2

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

NOW,

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

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

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

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

$\mathit{=3}$

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

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