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

$\frac{3}{2}$

5cosθ - 12 sinθ = 0

tanθ = \(\frac{5}{12}\)

By using pythagoras theorem  ,

P² + B² = H²

5² + 12² = H²

H = 13 

Now,

\(\frac{1 + sinθ + cosθ}{1 - sinθ + cosθ}\)

= \(\frac{1 + P/H + B/H}{1 - P/H + B/H}\)

= \(\frac{13 + 5 + 12}{13 - 5 + 12}\)

= \(\frac{30}{20}\)

= \(\frac{3}{2}\)