Simplify tan(x)^2(csc(x)^2-1)

Problem

tan(x)*(csc(x)−1)

Solution

1. Identify the trigonometric identity for the expression inside the parentheses.

2. Apply the identity csc(x)−1=cot(x) which is derived from the Pythagorean identity 1+cot(x)=csc(x)

tan(x)*(cot(x))

3. Use the reciprocal identity cot(x)=1/tan(x) to rewrite the expression.

tan(x)⋅1/tan(x)

4. Simplify the product by canceling the common terms.

1

Final Answer

tan(x)*(csc(x)−1)=1

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