To simplify the expression 1 - sin^2(x) on the left side of the equation, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1:

1 - sin^2(x) = cos^2(x)

Now we have:

cos^2(x) = sin(2x) / cos(x)

Using the double-angle identity sin(2x) = 2sin(x)cos(x), we get:

cos^2(x) = 2sin(x)cos(x) / cos(x)

Simplifying this expression further by canceling out the cos(x) terms on both sides, we have:

cos(x) = 2sin(x)

Therefore, the simplified equation is cos(x) = 2sin(x).