Question 55

If $$2 \sin \theta = 5 \cos \theta, then \dfrac{\sin \theta + \cos \theta}{\sin \theta - \cos \theta}$$ is equal to:

Solution

$$2\sin \theta = 5 \cos \theta$$

=>$$\dfrac{sin \theta}{\cos \theta} = \frac{5}{2}$$

=>$$\dfrac{\sin \theta + \cos \theta}{\sin \theta - \cos \theta}$$

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

= $$\dfrac{\frac{5}{2} + 1}{\frac{5}{2} -1}$$

=$$\dfrac{\frac{7}{2}}{\frac{3}{2}}$$

=$$\dfrac{7}{3}$$

So , the answer would be option d) 7:3

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