Verify the Identity sec(x)^2cot(x)-cot(x)=tan(x)

Problem

sec2(x)*cot(x)−cot(x)=tan(x)

Solution

1. Factor out the common term cot(x) from the left side of the equation.

cot(x)*(sec2(x)−1)

2. Apply the Pythagorean identity tan2(x)+1=sec2(x) which implies that sec2(x)−1=tan2(x)

cot(x)*tan2(x)

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

1/tan(x)⋅tan2(x)

4. Simplify the expression by canceling one factor of tan(x)

tan(x)

Final Answer

sec2(x)*cot(x)−cot(x)=tan(x)

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