Verify the Identity cot(y)^2(sec(y)^2-1)=1

Problem

cot2(y)*(sec2(y)−1)=1

Solution

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

2. Substitute the identity tan2(y)=sec2(y)−1 into the left side of the equation.

cot2(y)*(tan2(y))

3. Apply the reciprocal identity for the cotangent function, where cot(y)=1/tan(y)

(1/tan2(y))*tan2(y)

4. Simplify the expression by canceling the common terms in the numerator and denominator.

tan2(y)/tan2(y)=1

Final Answer

cot2(y)*(sec2(y)−1)=1

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