Simplify:$$ \frac{cos \theta}{(1 + sin \theta)}$$

$$ \frac{cos \theta}{(1 + sin \theta)}$$

Multiply top (numerator) and bottom(denominator) by 1 - sin θ

$$ \frac{{cos \theta}\times(1 - sin \theta)}{{(1 + sin \theta)}\times(1 - sin \theta)}$$

$$ \frac{{cos \theta} - {cos \theta}sin \theta)}{(1 - sin^2 \theta)}$$   ($$1 = sin^2 \theta+cos^2 \theta$$)

$$ \frac{{cos \theta} - {cos \theta}sin \theta)}{(cos^2 \theta)}$$

$$ \frac{cos \theta}{(cos^2 \theta)} - \frac{{cos \theta}sin \theta)}{(cos^2 \theta)}$$

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

$$sec \theta - tan\theta$$