Simplify 2csc(x)^2-1

Problem

2*csc2(x)−1

Solution

1. Identify the trigonometric identity for cosecant in terms of cotangent.

csc2(x)=1+cot2(x)

2. Substitute the identity into the original expression.

2*(1+cot2(x))−1

3. Distribute the constant 2 into the parentheses.

2+2*cot2(x)−1

4. Combine the constant terms to simplify the expression.

1+2*cot2(x)

Final Answer

2*csc2(x)−1=1+2*cot2(x)

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