Question

1/1+sin theta + 1/1-sin theta

Answer 1

Short answer 2 * sec^2(theta)
$\frac{1}{1 - sin(\theta)} + \frac{1}{1 + sin(\theta)}$
Find the common denominator
The common denominator is (1 - sin(theta) * (1 + sin(theta) )

Multiply each fraction's numerator and denominator by the common denominator

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

Remove the brackets and cancel the sin(theta) terms in the numerator.
Combine the denominator

2 / (1 - sin^2(theta)) but 1 - sin^2(theta) = cos^2(theta)
2 / (cos^2 (theta) but 1/cos^2(theta) = sec^2(theta)
2 * sec^2 (theta) <<<<< Answer