Question 659671
Start with the well known identity (you can easily prove it)
(1) sin^2(x) + cos^2(x) = 1
Now subtract sin^2(x) from each side and get
(2) cos^2(x) = 1 - sin^2(x)
Now factor the right side using the property
(3) (a^2-b^2) = (a+b)*(a-b), called the difference of two perfect squares in algebra (remember?), and get
(4) cos^2(x) = (1+sin(x))*(1-sin(x))  QED