Problem 18 of the Pre Test

Problem 18 is a clever and interesting problem. The way to solve it is by finding a common denominator by multiplying the denominators together. This will give the expression:

1(1 - sin x) + 1(1 + sin x)
___________________ =

(1 - sin x)(1 + sin x)

Now simplify:

2 /(1 - sin x + sin x - sinx^2 x)2 = 2/(1 - sin x) = 2/(cos^2 x) = 2 sec ^2