Question : If $5\tan\theta=4$, then $\frac{5\sin\theta-3\cos\theta}{5\sin\theta+2\cos\theta}$ is equal to:
Option 1: $\frac{2}{3}$
Option 2: $\frac{1}{4}$
Option 3: $\frac{1}{6}$
Option 4: $\frac{1}{3}$
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Correct Answer: $\frac{1}{6}$
Solution :
Given: $5\tan\theta = 4$
Now, $\frac{5\sin\theta-3\cos\theta}{5\sin\theta+2\cos\theta}$
= $\frac{5\frac{\sin\theta}{\cos\theta}-3}{5\frac{\sin\theta}{\cos\theta}+2}$
= $\frac{5\tan\theta-3}{5\tan\theta+2}$
= $\frac{4 - 3}{4 +2}$
= $\frac{1}{6}$
Hence, the correct answer is $\frac{1}{6}$.
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