Solve for x tan(x)cot(x)=1

Problem

tan(x)*cot(x)=1

Solution

1. Identify the trigonometric identity for the cotangent function.

cot(x)=1/tan(x)

2. Substitute the identity into the original equation.

tan(x)⋅1/tan(x)=1

3. Simplify the left side of the equation by canceling the common factor.

1=1

4. Determine the domain constraints, as the expression is undefined where the functions are undefined.

tan(x)≠0

cot(x)≠0

Final Answer

tan(x)*cot(x)=1* for *x≠(n*π)/2

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