$\frac{1+\sin \theta}{\cos \theta}$ is equal to which of the following (where $\theta \neq \frac{\pi}{2}$) ?

$\frac{\cos \theta}{1-\sin \theta}$

Given :-

 \(\frac{1 + sin θ}{cos θ}\)

Multiply and divide by ( 1 - sin θ )

 = \(\frac{1 + sin θ}{cos θ}\) ×  \(\frac{1 - sin θ}{1 - sin θ}\)

= \(\frac{(1² - sin² θ}{cos θ ( 1 - sin θ)}\)

= \(\frac{(cos² θ}{cos θ ( 1 - sin θ)}\)

= \(\frac{(cos θ}{( 1 - sin θ)}\)

So , Option 4 is correct .