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

Problem

tan(x)=cot(x)

Solution

1. Rewrite the equation using the reciprocal identity cot(x)=1/tan(x)

tan(x)=1/tan(x)

2. Multiply both sides by tan(x) to eliminate the fraction, noting that tan(x) cannot be zero.

tan2(x)=1

3. Take the square root of both sides to solve for tan(x)

tan(x)=±1

4. Identify the angles where the tangent function equals 1 or −1

tan(x)=1⇒x=π/4+n*π

tan(x)=−1⇒x=−π/4+n*π

5. Combine the solutions into a single general expression.

x=π/4+(n*π)/2

Final Answer

tan(x)=cot(x)⇒x=π/4+(n*π)/2,n∈ℤ

Want more problems? Check here!