Question 66

If $$3 \sin \theta = 2 \cos \theta, then \frac{4 \sin \theta - \cos \theta}{4 \cos \theta + \sin \theta}$$ is equal to:

Solution

$$3 \sin \theta = 2 \cos \theta$$

$$\frac{\sin \theta}{\cos \theta} =\frac{2}{3}$$

$$ \frac{4 \sin \theta - \cos \theta}{4 \cos \theta + \sin \theta}$$

Divide both numerator and denominator by $$\cos\theta$$ ,

$$\frac{4\tan \theta -1 }{4 + \tan \theta}$$

= $$\frac{5}{14}$$

So , the answer would be option c)$$\frac{5}{14}$$.

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