If $$5 \cos \theta - 12 \sin \theta = 0$$, then what is the value of $$\frac{1 + \sin \theta + \cos \theta}{1 - \sin \theta + \cos \theta}$$

$$5 \cos \theta - 12 \sin \theta = 0$$

$$tan \theta = \frac{5}{12}$$

We know that $$tan \theta = \dfrac{perpendicular}{base}$$ so,

By the triplet 5-12-13,

Hypotenuse = 13

$$sin \theta = \dfrac{5}{13}$$

$$cos \theta = \dfrac{12}{13}$$

$$\dfrac{1 + \sin \theta + \cos \theta}{1 - \sin \theta + \cos \theta}$$

= $$\dfrac{1 + \dfrac{5}{13} + \dfrac{12}{13}}{1 -  \dfrac{5}{13} + \dfrac{12}{13}}$$

= $$\dfrac{30}{20} = \dfrac{3}{2}$$