Final answer:
To solve the given equation, simplify the expression and use the trigonometric identity to substitute for the cosine terms. Then, solve the resulting quadratic equation for x.
Step-by-step explanation:
To solve the equation (sin2x+sinx)/(cos2x+cosx+1)=2cosx, we can start by simplifying the expression. First, multiply both sides of the equation by the denominator (cos2x+cosx+1) to get rid of the fraction. This gives us sin2x+sinx=2cosx*(cos2x+cosx+1). Next, distribute the 2cosx into the parentheses on the right side of the equation. After simplifying and rearranging the terms, we can use the trigonometric identity tan(x) = sin(x)/cos(x) to substitute for the cosine terms. Solving the resulting quadratic equation will give the values of x.