To simplify the left side of the equation, we can use the double angle formula for cosine and the product-to-sum formula for sine.

cos(2x) = 2cos^2(x) - 1
sin(x) * cos(x) = 0.5sin(2x)

Therefore, the original equation becomes:
2cos^2(x) - 1 + 0.5sin(2x) = 1 + 0.5sin(2x)

Now we have:
2cos^2(x) - 1 = 1
2cos^2(x) = 2
cos^2(x) = 1
cos(x) = ± 1

So, the solution to the equation is:
x = ± π/2 + 2nπ, where n is an integer.