Question 53

If $$ 3 \tan\theta = 2 $$ , find the value of $$ \frac{2\sin\theta - \cos\theta}{2\cos\theta - \sin\theta} $$ .

Solution

$$3 \tan\theta = 2 $$ => $$\tan\theta = \frac{2}{3} $$

$$ \cot\theta= \frac{3}{2} $$

$$ \frac{2\sin\theta - \cos\theta}{2\cos\theta - \sin\theta} $$

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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