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) - 1sin(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 = 12cos^2(x) = 2cos^2(x) = 1cos(x) = ± 1
So, the solution to the equation is:x = ± π/2 + 2nπ, where n is an integer.
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.