Final answer:
To verify the equation, expand the square of the numerator, simplify both sides using trigonometric identities, and compare the simplified expressions.
Step-by-step explanation:
To verify the given equation (sin(x) + cos(x))^2 / sin(2x) = csc(2x) + 1, we can simplify both sides of the equation separately and compare them. We can start by expanding the square of the numerator on the left side of the equation using the binomial theorem. Next, we can use multiple trigonometric identities to simplify both sides of the equation further. Finally, we can compare the simplified expressions on both sides to verify if they are equal.