Solve this
Question:

If $5 \tan \theta=3$ then $\left(\frac{5 \sin \theta-\cos \theta}{5 \sin \theta+\cos \theta}\right)=?$

(a) $\frac{2}{3}$

(b) $\frac{1}{3}$

(c) $\frac{1}{2}$

(d) $\frac{3}{5}$

 

Solution:

$5 \tan \theta=3$

$\Rightarrow 5 \times \frac{\sin \theta}{\cos \theta}=3$

$\Rightarrow 5 \sin \theta=3 \cos \theta \quad \ldots \ldots(1)$

$\therefore \frac{5 \sin \theta-\cos \theta}{5 \sin \theta+\cos \theta}$

$=\frac{3 \cos \theta-\cos \theta}{3 \cos \theta+\cos \theta} \quad[$ Using $(1)]$

$=\frac{2 \cos \theta}{4 \cos \theta}$

$=\frac{1}{2}$

Hence, the correct answer is option (c).

 

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