Which of the following expressions is not equivalent to cot2θ?csc 2θ + 1( ) 2csc 2θ - 1

To determine which of the given expressions is not equivalent to cot(2θ), we can simplify each expression and compare them.

1. csc(2θ) + 1: To simplify this expression, we need to find the reciprocal of sin(2θ), which is csc(2θ). Adding 1 to it, we get csc(2θ) + 1. However, this expression is not equivalent to cot(2θ) because cot(2θ) is equal to 1 / tan(2θ), not 1 + csc(2θ).

2. 2csc(2θ) - 1: Similarly, we can simplify this expression by finding the reciprocal of sin(2θ), which is csc(2θ). Multiplying it by 2 and subtracting 1, we get 2csc(2θ) - 1. This expression is also not equivalent to cot(2θ) because cot(2θ) is equal to 1 / tan(2θ), not 2csc(2θ) - 1.

Therefore, neither of the given expressions is equivalent to cot(2θ).