Question

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Answer 1

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

$\sf{\displaystyle \: \tan \theta = \frac{ \sin \theta}{ \cos \theta} }$

GIVEN

$\sf{\displaystyle \: \tan \theta = \frac{1}{2} }$

TO DETERMINE

$\sf{\displaystyle \: \: \frac{2\sin \theta + 3 \cos \theta}{4\cos \theta + \: 3\sin \theta } }$

EVALUATION

$\sf{\displaystyle \: \: \frac{2\sin \theta + 3 \cos \theta}{4\cos \theta + \: 3\sin \theta } }$

Dividing numerator and denominator both by

$\cos \theta$

We get

$= \sf{\displaystyle \: \: \frac{2 \times \frac{\sin \theta}{\cos \theta} + 3 }{4 + \: 3 \times \frac{\sin \theta}{\cos \theta} } }$

$= \sf{\displaystyle \: \: \frac{2\tan \theta + 3}{4 + \: 3\tan \theta } }$

$= \sf{\displaystyle \: \: \frac{2 \times \frac{1}{2} + 3}{4 + \: 3 \times \frac{1}{2} } }$

$= \sf{\displaystyle \: \: \frac{1+ 3}{4 + \frac{3}{2} } }$

$= \sf{\displaystyle \: \: \frac{4}{ \frac{8 + 3}{2} } }$

$= \sf{\displaystyle \: \: \frac{8}{ 11 } }$