If $$ 3 \tan\theta = 2 $$ , find the value of $$ \frac{2\sin\theta - \cos\theta}{2\cos\theta - \sin\theta} $$ .
$$3 \tan\theta = 2 $$ =>Â $$\tan\theta = \frac{2}{3} $$
$$ \cot\theta=Â \frac{3}{2} $$
$$ \frac{2\sin\theta - \cos\theta}{2\cos\theta - \sin\theta} $$
Diving numerator and denominator by $$ \cos\theta$$,
$$ \frac{2\tan\theta - 1}{2 - \tan\theta} $$
= $$ \frac{2\times \frac{2}{3} - 1}{2 - \frac{2}{3}} $$
=$$ \frac{1}{4} $$
So, the answer would be Option c)$$ \frac{1}{4} $$.
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