Final answer:
To verify the identity, we need to simplify both sides of the equation. By applying trigonometric identities and simplifying, we can show that the left side is equal to the right side. The identity is true.
Step-by-step explanation:
To verify the identity, we need to simplify the left side of the equation and show that it is equal to the right side.
Starting with the left side, we have cot²(x) / csc(x) + 1.
Using the trigonometric identities csc(x) = 1/sin(x) and cot(x) = 1/tan(x), we can rewrite the expression as (1/tan(x))² / (1/sin(x)) + 1.
Simplifying further, we get sin²(x) / tan²(x) + 1.
Using the identity tan²(x) = 1 - cos²(x), we substitute and obtain sin²(x) / (1 - cos²(x)) + 1.
Now, we can simplify the right side of the equation.
Using the identity 1 - sin(x) = cos²(x), we can rewrite the expression as cos²(x) / (1 - cos²(x)).
We can see that the left side of the equation is equal to the right side. Therefore, the identity is true. The answer is a) True.