Solve for x tan(x)-3cot(x)=0

Problem

tan(x)−3*cot(x)=0

Solution

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

tan(x)−3/tan(x)=0

2. Multiply the entire equation by tan(x) to eliminate the fraction, assuming tan(x)≠0

tan2(x)−3=0

3. Isolate the squared term by adding 3 to both sides.

tan2(x)=3

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

tan(x)=±√(,3)

5. Determine the values of x that satisfy the equation within the standard period.

x=π/3+n*π

x=−π/3+n*π

6. Combine the solutions into a single general expression where n is an integer.

x=π/3+n*π,−π/3+n*π

Final Answer

tan(x)−3*cot(x)=0⇒x=π/3+n*π,(2*π)/3+n*π

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