Simplify 1/(sin(A)^2)-1/(tan(A)^2)

Problem

1/sin2(A)−1/tan2(A)

Solution

1. Identify the reciprocal identities for the given trigonometric functions.

1/sin2(A)=csc2(A)

1/tan2(A)=cot2(A)

2. Substitute these identities into the original expression.

csc2(A)−cot2(A)

3. Apply the Pythagorean identity relating cosecant and cotangent.

1+cot2(A)=csc2(A)

4. Rearrange the identity to solve for the expression.

csc2(A)−cot2(A)=1

Final Answer

1/sin2(A)−1/tan2(A)=1

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